Earnings per Share - Schedule of Earnings Per Share - Basic and Diluted (Details) - USD ($) $ / shares in Units, $ in Thousands	3 Months Ended		9 Months Ended
	Dec. 31, 2021	Dec. 31, 2020	Dec. 31, 2021	Dec. 31, 2020
Net income attributable to Class A Stockholders
Net income attributable to HLI	$ 51,849	$ 33,203	$ 132,161	$ 58,263
Common Class A
Net income attributable to Class A Stockholders
Net income attributable to HLI	51,849	33,203	132,161	58,263
Impact of changes in carrying amount of redeemable NCI	1,308	0	358	0
Basic EPS of Class A common stock	53,157	33,203	132,519	58,263
Assumed vesting of employee awards	66	94	156	156
Assumed conversion of Class B and Class C Units	21,946	0	60,083	0
Diluted EPS of Class A common stock	$ 75,169	$ 33,297	$ 192,758	$ 58,419
Weighted-Average Shares
Weighted-average basic EPS of Class A common stock (in shares)	36,902,741	34,478,437	36,375,797	32,567,754
Weighted-average assumed vesting of employee awards (in shares)	165,569	272,955	138,902	240,194
Weighted-average assumed conversion of Class B and Class C units (in shares)	16,675,834	0	17,192,702	0
Weighted-average diluted EPS of Class A common stock (in shares)	53,744,144	34,751,392	53,707,401	32,807,948
Per share amount
Basic EPS of Class A common stock (in dollars per share)	$ 1.44	$ 0.96	$ 3.64	$ 1.79
Diluted EPS of Class A common stock (in dollars per share)	$ 1.40	$ 0.96	$ 3.59	$ 1.78