Revenue Recognition (Narrative) (Details) - USD ($) $ in Millions	3 Months Ended
Nov. 30, 2022	Nov. 30, 2021	Aug. 31, 2022
Disaggregation Of Revenue [Line Items]
Unsatisfied performance obligation amount	$ 1.8
Revenue recognized	17.9	$ 12.7
Other Current Assets [Member]
Disaggregation Of Revenue [Line Items]
Contract assets	1.1	1.2	$ 0.9
Other Current Liabilities [Member]
Disaggregation Of Revenue [Line Items]
Contract liabilities	$ 27.5	$ 41.1	$ 30.6

Contract with customer unsatisfied performance obligation amount.

No definition available.

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Namespace Prefix:	lnn_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Amount, after allowance for credit loss, of right to consideration in exchange for good or service transferred to customer when right is conditioned on something other than passage of time.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 606
-SubTopic 10
-Section 50
-Paragraph 8
-Subparagraph (a)
-URI https://asc.fasb.org/extlink&oid=126920106&loc=SL49130549-203045

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 606
-SubTopic 10
-Section 45
-Paragraph 1
-URI https://asc.fasb.org/extlink&oid=126919976&loc=SL49130531-203044

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 606
-SubTopic 10
-Section 45
-Paragraph 3
-URI https://asc.fasb.org/extlink&oid=126919976&loc=SL49130533-203044

+ Details

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Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount of obligation to transfer good or service to customer for which consideration has been received or is receivable.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 606
-SubTopic 10
-Section 45
-Paragraph 1
-URI https://asc.fasb.org/extlink&oid=126919976&loc=SL49130531-203044

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 606
-SubTopic 10
-Section 50
-Paragraph 8
-Subparagraph (a)
-URI https://asc.fasb.org/extlink&oid=126920106&loc=SL49130549-203045

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 606
-SubTopic 10
-Section 45
-Paragraph 2
-URI https://asc.fasb.org/extlink&oid=126919976&loc=SL49130532-203044

+ Details

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Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Amount of revenue recognized that was previously included in balance of obligation to transfer good or service to customer for which consideration from customer has been received or is due.

+ References

+ Details

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Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

+ References

No definition available.

+ Details

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- Details

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