Earnings per Share - Schedule of Earnings Per Share, Basic and Diluted (Details) - USD ($) $ / shares in Units, $ in Thousands	3 Months Ended		6 Months Ended
	Sep. 30, 2023	Sep. 30, 2022	Sep. 30, 2023	Sep. 30, 2022
Net income attributable to Class A Stockholders
Net income attributable to HLI	$ 41,994	$ 34,881	$ 72,992	$ 68,365
Class A Common Stock
Net income attributable to Class A Stockholders
Net income attributable to HLI	41,994	34,881	72,992	68,365
Impact of changes in carrying amount of redeemable NCI	0	1,333	0	1,713
Basic EPS of Class A common stock	41,994	36,214	72,992	70,078
Assumed vesting of employee awards	44	17	53	9
Assumed conversion of Class B and Class C Units	17,824	15,825	30,177	31,007
Diluted EPS of Class A common stock	$ 59,862	$ 52,056	$ 103,222	$ 101,094
Weighted-Average Shares
Weighted-average basic EPS of Class A common stock (in shares)	37,718,210	37,009,309	37,713,038	37,000,150
Weighted-average assumed vesting of employee awards (in shares)	133,775	60,790	94,622	48,816
Weighted-average assumed conversion of Class B and Class C units (in shares)	16,089,097	16,675,834	16,089,097	16,675,834
Weighted-average diluted EPS of Class A common stock (in shares)	53,941,082	53,745,933	53,896,757	53,724,800
Per share amount
Basic EPS of Class A common stock (in dollars per share)	$ 1.11	$ 0.98	$ 1.94	$ 1.89
Diluted EPS of Class A common stock (in dollars per share)	$ 1.11	$ 0.97	$ 1.92	$ 1.88