Earnings per Share - Schedule of Earnings Per Share - Basic and Diluted (Details) - USD ($) $ / shares in Units, $ in Thousands	3 Months Ended								12 Months Ended
	Mar. 31, 2021	Dec. 31, 2020	Sep. 30, 2020	Jun. 30, 2020	Mar. 31, 2020	Dec. 31, 2019	Sep. 30, 2019	Jun. 30, 2019	Mar. 31, 2021	Mar. 31, 2020	Mar. 31, 2019
Numerator
Net income attributable to HLI	$ 39,760	$ 33,203	$ 21,813	$ 3,246	$ 20,648	$ 13,497	$ 15,299	$ 11,381	$ 98,022	$ 60,825	$ 33,573
Less: Deemed dividend for the accretion of redeemable non-controlling interest									(4,637)	0	0
Net income attributable to Class A common stockholders - basic									93,385	60,825	33,573
Numerator
Net income attributable to Class A common stockholders - basic									93,385	60,825	33,573
Net income attributable to Class A common stockholders - diluted									$ 93,614	$ 61,177	$ 33,928
Denominator
Diluted earnings per share (in dollars per share)									$ 2.81	$ 2.15	$ 1.40
Common Class A
Numerator
Net income attributable to HLI									$ 98,022	$ 60,825	$ 33,573
Denominator
Weighted-average shares of Class A common stock outstanding (in shares)									33,152,318	28,088,578	23,836,401
Basic earnings per share (in dollars per share)	$ 1.01	$ 0.96	$ 0.66	$ 0.11	$ 0.71	$ 0.46	$ 0.56	$ 0.43	$ 2.82	$ 2.17	$ 1.41
Numerator
Assumed vesting of employee awards									$ 229	$ 352	$ 355
Denominator
Weighted-average shares of Class A common stock outstanding (in shares)									33,152,318	28,088,578	23,836,401
Assumed vesting of employee awards (in shares)									210,047	350,194	462,394
Weighted-average shares of Class A common stock outstanding - diluted (in shares)									33,362,365	28,438,772	24,298,795
Diluted earnings per share (in dollars per share)	$ 1.00	$ 0.96	$ 0.66	$ 0.11	$ 0.70	$ 0.46	$ 0.56	$ 0.42	$ 2.81	$ 2.15	$ 1.40