Earnings per Share - Schedule of Earnings Per Share - Basic and Diluted (Details) - USD ($) $ / shares in Units, $ in Thousands	3 Months Ended
	Jun. 30, 2022	Jun. 30, 2021
Net income attributable to Class A Stockholders
Net income attributable to HLI	$ 33,484	$ 28,168
Class A Common Stock
Net income attributable to Class A Stockholders
Net income attributable to HLI	33,484	28,168
Impact of changes in carrying amount of redeemable NCI	380	0
Basic EPS of Class A common stock	33,864	28,168
Assumed vesting of employee awards	9
Assumed conversion of Class B and Class C Units	15,179	34
Diluted EPS of Class A common stock	$ 49,052	$ 28,202
Weighted-Average Shares
Weighted-average basic EPS of Class A common stock (in shares)	36,999,561	36,003,089
Weighted-average assumed vesting of employee awards (in shares)	31,546	125,905
Weighted-average assumed conversion of Class B and Class C units (in shares)	16,675,834
Weighted-average diluted EPS of Class A common stock (in shares)	53,706,941	36,128,994
Per share amount
Basic EPS of Class A common stock (in dollars per share)	$ 0.92	$ 0.78
Diluted EPS of Class A common stock (in dollars per share)	$ 0.91	$ 0.78