Earnings per Share - Schedule of Earnings Per Share - Basic and Diluted (Details) - USD ($) $ / shares in Units, $ in Thousands	3 Months Ended
	Jun. 30, 2023	Jun. 30, 2022
Net income attributable to Class A Stockholders
Net income attributable to HLI	$ 30,998	$ 33,484
Class A Common Stock
Net income attributable to Class A Stockholders
Net income attributable to HLI	30,998	33,484
Impact of changes in carrying amount of redeemable NCI	0	380
Basic EPS of Class A common stock	30,998	33,864
Assumed vesting of employee awards	14	9
Assumed conversion of Class B and Class C Units	12,602	15,179
Diluted EPS of Class A common stock	$ 43,614	$ 49,052
Weighted-Average Shares
Weighted-average basic EPS of Class A common stock (in shares)	37,707,809	36,999,561
Weighted-average assumed vesting of employee awards (in shares)	58,845	31,546
Weighted-average assumed conversion of Class B and Class C units (in shares)	16,089,097	16,675,834
Weighted-average diluted EPS of Class A common stock (in shares)	53,855,751	53,706,941
Per share amount
Basic EPS of Class A common stock (in dollars per share)	$ 0.82	$ 0.92
Diluted EPS of Class A common stock (in dollars per share)	$ 0.81	$ 0.91