Under the Securities Exchange Act of 1934
(Amendment No. 1 )*

Triton International Limited

(Name of Issuer)

Common Shares, par value $0.01 per share

(Title of Class of Securities)

G9078F107

(CUSIP Number)

Steven Della Rocca, Esq.

Vestar Capital Partners LLC

245 Park Avenue, 41st Floor

New York, New York 10167

Telephone: (212) 351-1600

with a copy to:

Christopher E. Austin

Neil R. Markel

Cleary Gottlieb Steen & Hamilton LLP

One Liberty Plaza

New York, New York 10006

Telephone: (212) 225-2000

(Name, Address and Telephone Number of Person
Authorized to Receive Notices and Communications)

September 5, 2017

(Date of Event Which Requires Filing of this Statement)

If the filing person has previously filed a statement on Schedule 13G to report the acquisition that is the subject of this Schedule 13D, and is filing this schedule because §§ 240.13d-1(e), 240.13d-1(f) or 240.13d-1(g) check the following box. ☐

Note: Schedules filed in paper format shall include a signed original and five copies of the schedule, including all exhibits. See § 240.13d-7(b) for other parties to whom copies are to be sent.

* The remainder of this cover page shall be filled out for a reporting person's initial filing on this form with respect to the subject class of securities, and for any subsequent amendment containing information which would alter disclosures provided in a prior cover page.

The information required on the remainder of this cover page shall not be deemed to be "filed" for the purpose of Section 18 of the Securities Exchange Act of 1934 ("Act") or otherwise subject to the liabilities of that section of the Act but shall be subject to all other provisions of the Act (however, see the Notes).

SCHEDULE 13D

 * The calculation assumes that there are a total of 74,536,402 Common Shares (as defined below) outstanding, as reported in the Issuer’s preliminary prospectus supplement on Form 424B3 filed with the Securities and Exchange Commission (the “Commission”) on September 5, 2017.

SCHEDULE 13D

* The calculation assumes that there are a total of 74,536,402 Common Shares (as defined below) outstanding, as reported in the Issuer’s preliminary prospectus supplement on Form 424B3 filed with the Commission on September 5, 2017.

SCHEDULE 13D

* The calculation assumes that there are a total of 74,536,402 Common Shares (as defined below) outstanding, as reported in the Issuer’s preliminary prospectus supplement on Form 424B3 filed with the Commission on September 5, 2017.

SCHEDULE 13D

 * The calculation assumes that there are a total of 74,536,402 Common Shares (as defined below) outstanding, as reported in the Issuer’s preliminary prospectus supplement on Form 424B3 filed with the Commission on September 5, 2017.

SCHEDULE 13D

 * The calculation assumes that there are a total of 74,536,402 Common Shares (as defined below) outstanding, as reported in the Issuer’s preliminary prospectus supplement on Form 424B3 filed with the Commission on September 5, 2017.

SCHEDULE 13D

 * The calculation assumes that there are a total of 74,536,402 Common Shares (as defined below) outstanding, as reported in the Issuer’s preliminary prospectus supplement on Form 424B3 filed with the Commission on September 5, 2017.

SCHEDULE 13D

 * The calculation assumes that there are a total of 74,536,402 Common Shares (as defined below) outstanding, as reported in the Issuer’s preliminary prospectus supplement on Form 424B3 filed with the Commission on September 5, 2017.

SCHEDULE 13D

 * The calculation assumes that there are a total of 74,536,402 Common Shares (as defined below) outstanding, as reported in the Issuer’s preliminary prospectus supplement on Form 424B3 filed with the Commission on September 5, 2017.

SCHEDULE 13D

 * The calculation assumes that there are a total of 74,536,402 Common Shares (as defined below) outstanding, as reported in the Issuer’s preliminary prospectus supplement on Form 424B3 filed with the Commission on September 5, 2017.

SCHEDULE 13D

 * The calculation assumes that there are a total of 74,536,402 Common Shares (as defined below) outstanding, as reported in the Issuer’s preliminary prospectus supplement on Form 424B3 filed with the Commission on September 5, 2017.

This Amendment No. 1 (this “Amendment”) amends and supplements the Schedule 13D filed by the Reporting Persons on September 19, 2016 (the “Original Schedule 13D” and, as amended and supplemented by this Amendment, the “Schedule 13D”) with respect to the Common Shares of the Issuer. Capitalized terms used in this Amendment and not otherwise defined herein shall have the same meanings ascribed to them in the Original Schedule 13D.

Item 2.  Identity and Background.

The response set forth in Item 2 of the Schedule 13D is hereby amended by deleting Schedule 1 in its entirety, and replacing it with Schedule 1 attached hereto.

This Amendment amends and restates the second paragraph of Item 2 in its entirely as set forth below.

“Vestar Luxco is the sole member of Vestar Gibco, which holds 10,479,601 Common Shares. Vestar Holdings is the sole member of Vestar Luxco. Vestar Capital V is the general partner of Vestar Holdings. Vestar Associates V is the general partner of Vestar Capital V. VMV is the general partner of both Vestar Associates V and Vestar/Triton Investments, which holds 200,924 Common Shares. VMV has voting and investment power over the Common Shares held or controlled by each of Vestar Investments and Vestar Gibco. Vestar Management II holds a majority of the outstanding membership interests of VCP, which holds 12,250 Common Shares. Daniel S. O'Connell is the sole director of VMV and the sole owner of Vestar Management II, and as a result he may be deemed to share beneficial ownership of the Common Shares held directly by the aforementioned Vestar entities.”

Item 3.  Source and Amount of Funds or Other Consideration.

This Amendment amends and restates the third paragraph of Item 3 in its entirely as set forth below.

“On September 7, 2016, VCP received 6,725 Common Shares in exchange for director services provided by Mr. Robert Rosner to the Issuer. On May 10, 2017, VCP received 5,525 Common Shares in exchange for director services provided by Mr. Robert Rosner to the Issuer. Mr. Rosner is the current designee to the board of directors of the Issuer (the “Board”) by the Reporting Persons and serves as the Lead Director of the Board.”

Item 5. Interest in Securities of the Issuer

This Amendment amends and restates the second and third paragraphs of Item 5 in their entirely as set forth below.

The following disclosure assumes that there are a total of 74,536,402 Common Shares (as defined below) outstanding, as reported in the Issuer’s preliminary prospectus supplement on Form 424B3 filed with the Commission on September 5, 2017.

Pursuant to Rule 13d-3 under the Exchange Act, the Reporting Persons may be deemed to beneficially own, in the aggregate, 10,692,775 Common Shares, which constitutes approximately 14.35% of the outstanding Common Share.

Item 6.  Contracts, Arrangements, Understandings or Relationships with Respect to Securities of the Issuer

This Amendment amends and restates the tenth paragraph of Item 6 of the Original Schedule 13D in its entirety as set forth below

 “Lock-up Agreement

In connection with the registered underwritten offering undertaken by the Issuer on September 5, 2017, Vestar/Triton Investments, Vestar Gibco, VCP, , certain other shareholders of the Issuer and each director and officer of the Issuer agreed with Merrill Lynch, Pierce, Fenner & Smith Incorporated (“Merrill Lynch”) and the other underwriters of the offering, subject to certain exceptions, not to dispose of or hedge any of their Common

Shares or securities convertible into or exchangeable for Common Shares for a period ending on the date that is 60 days following the date of the underwriting agreement, except with the prior written consent of Merrill Lynch. Merrill Lynch may in its sole discretion and at any time without notice release some or all of the shares subject to a Lock-Up Agreement prior to the expiration of the lock-up period.

The foregoing description of the terms of the Shareholders Agreement and the Lock-Up Agreement are not intended to be complete and are qualified in their entirety by reference to the full text of the Shareholders Agreement, which is filed as Exhibit C and incorporated herein by reference, and the form of the Lock-Up Agreement, which is filed as Exhibit D and incorporated herein by reference.”

Item 7.  Material to be Filed as Exhibits

 This Amendment amends and restates Item 7 of the Original Schedule 13D in its entirety as set forth below:

SIGNATURE

After reasonable inquiry and to the best of my knowledge and belief, I certify that the information set forth in this Statement is true, complete and correct.

Dated: September 7, 2017

(1) Mr. Steven Della Rocca is signing pursuant to a power of attorney dated July 12, 2016, which was previously filed with the Securities and Exchange Commission as an exhibit to the Initial Statement of Beneficial Ownership of Securities on Form 3 filed by (i) Vestar/Triton Investments III, L.P., (ii) Vestar-Triton (Gibco) Limited, (iii) Triton-Vestar Luxco S.a.r.L., (iv) Vestar/Triton Investments Holdings L.P. (v) Vestar Capital Partners V, L.P., (vi) Vestar Associates V, L.P. (vii) Vestar Managers V Ltd. and (vii) Daniel S. O’Connell on July 12, 2016 (SEC File No. 001-37827).

(2) Mr. Steven Della Rocca is signing pursuant to a power of attorney dated September 19, 2016, which was previously filed with the Securities and Exchange Commission as an exhibit to the Original Schedule 13D.

SCHEDULE A

CERTAIN INFORMATION CONCERNING EXECUTIVE OFFICERS AND DIRECTORS OF THE REPORTING PERSONS

*Unless indicated otherwise, all individuals listed in this Schedule A are citizens of the United States

**The business address of all individuals listed in this Schedule A is c/o Vestar Capital Partners LLC, 245 Park Avenue, 41st Floor, New York, New York 10167.

Daniel S. O’Connell, sole director and Chief Executive Officer

Norman W. Alpert, Co-President

Robert L. Rosner, Co-President

Steven Della Rocca, Managing Director and General Counsel

James L. Elrod, Jr., Managing Director

Roger C. Holstein, Managing Director

James P. Kelley, Managing Director

Kevin Mundt, Managing Director

Kenneth J. O’Keefe, Managing Director and Chief Operating Officer

Chris Durbin, Managing Director

Brian O’Connor, Managing Director

John Stephens, Managing Director

Brian P. Schwartz, Managing Director

Brendan J. Spillane, Managing Director

INDEX TO EXHIBITS

September 5, 2017

Merrill Lynch, Pierce, Fenner & Smith
                Incorporated
Wells Fargo Securities, LLC
RBC Capital Markets, LLC

as Representatives of the several
Underwriters to be named in the
within-mentioned Underwriting Agreement

c/o Merrill Lynch, Pierce, Fenner & Smith
                      Incorporated
One Bryant Park
New York, New York 10036

c/o Wells Fargo Securities, LLC

375 Park Avenue

4th Floor

New York, New York 10152

c/o RBC Capital Markets, LLC

200 Vesey Street

10th Floor

New York, New York 10281

Re: Proposed Public Offering by Triton International Limited

Dear Sirs:

The undersigned, a stockholder of Triton International Limited, a Bermuda company (the “Company”), understands that Merrill Lynch, Pierce, Fenner & Smith Incorporated (“Merrill Lynch”), Wells Fargo Securities, LLC (“Wells Fargo”) and RBC Capital Markets, LLC (“RBC”) propose to enter into an Underwriting Agreement (the “Underwriting Agreement”) with the Company and the Selling Shareholders providing for the public offering of shares of the Company’s common shares, par value $0.01 per share (the “Common Shares”). In recognition of the benefit that such an offering will confer upon the undersigned as a stockholder [and an officer and/or director] of the Company, and for other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the undersigned agrees with each underwriter to be named in the Underwriting Agreement that, during the period beginning on the date hereof and ending on the date that is 60 days from the date of the Underwriting Agreement (subject to extensions as discussed below) (the “Lock-Up Period”), the undersigned will not, without the prior written consent of Merrill Lynch, (i) directly or indirectly, offer, pledge, sell, contract to sell, sell any option or contract to purchase, purchase any option or contract to sell, grant any option, right or warrant to purchase or otherwise transfer or dispose of any shares of the Company’s Common Shares or any securities convertible into or exercisable or exchangeable for Common Shares, whether now owned or hereafter acquired by the undersigned or with respect to which the undersigned has or hereafter acquires the power of disposition (collectively, the “Lock-Up Securities”), or exercise any right with respect to the registration of any of the Lock-up Securities, or file or cause to be filed any registration statement in connection therewith, under the Securities Act of 1933, as amended, or (ii) enter into any swap or any other agreement or any transaction that transfers, in whole or in part, directly or indirectly, the economic consequence of ownership of the Lock-Up Securities, whether any such swap or transaction is to be settled by delivery of Common Shares or other securities, in cash or otherwise.

Notwithstanding the foregoing, and subject to the conditions below, the undersigned may transfer the Lock-Up Securities without the prior written consent of Merrill Lynch, provided that (1) except in the case of clauses (viii) through (x) below, Merrill Lynch receives a signed lock-up agreement for the balance of the lockup period from each donee, trustee, distributee, or transferee, as the case may be, (2) except in the case of clauses (viii) through (x) below, any such transfer shall not involve a disposition for value, (3) except in the case of clauses (viii) through (x) below, such transfers are not required to be reported with the Securities and Exchange Commission on Form 4 in accordance with Section 16 of the Securities Exchange Act of 1934, as amended (the “Exchange Act”), (4) the undersigned does not otherwise voluntarily effect any public filing or report regarding such transfers and (5) in the case of clauses (viii) through (x) below, any Form 4 filed in connection therewith contain a footnote indicating that such filing relates to the circumstances described therein:

(i)                 to the Underwriters pursuant to the Underwriting Agreement;

Furthermore, the undersigned may sell Common Shares of the Company purchased by the undersigned on the open market following the Public Offering if and only if (i) such sales are not required to be reported in any public report or filing with the Securities and Exchange Commission, or otherwise and (ii) the undersigned does not otherwise voluntarily effect any public filing or report regarding such sales.

The undersigned also agrees and consents to the entry of stop transfer instructions with the Company’s transfer agent and registrar against the transfer of the Lock-Up Securities except in compliance with the foregoing restrictions.

Notwithstanding anything to the contrary contained herein, this lock-up agreement will automatically terminate and the undersigned will be released from all of his, her or its obligations hereunder upon the earliest to occur, if any, of the following: (i) prior to the execution of the Underwriting Agreement, the Company advises Merrill Lynch in writing, that it has determined not to proceed with the Public Offering, (ii) the Underwriting Agreement is executed but is terminated (other than with respect to the provisions thereof which survive termination) prior to payment for and delivery of the Lock-Up Securities to be sold thereunder or (iii) September 30, 2017, in the event that the Underwriting Agreement has not been executed by such date.

This lock-up agreement will be governed by and construed in accordance with the laws of the State of New York applicable to contracts made and to be performed within the State of New York.

[Signature Page Follows]

Very truly yours,

Signature:                             

Print Name: