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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, 2023
Dec. 31, 2022
Dec. 31, 2023
Dec. 31, 2022
Net income attributable to Class A Stockholders        
Net income attributable to HLI $ 19,506 $ 9,669 $ 92,498 $ 78,034
Class A Common Stock        
Net income attributable to Class A Stockholders        
Net income attributable to HLI 19,506 9,669 92,498 78,034
Impact of changes in carrying amount of redeemable NCI 0 2,095 0 3,809
Basic EPS of Class A common stock 19,506 11,764 92,498 81,843
Assumed vesting of employee awards 25 5 88 34
Assumed conversion of Class B and Class C Units 8,232 5,058 38,456 35,968
Diluted EPS of Class A common stock $ 27,763 $ 16,827 $ 131,042 $ 117,845
Weighted-Average Shares        
Weighted-average basic EPS of Class A common stock (in shares) 37,736,012 37,025,416 37,720,724 37,004,657
Weighted-average assumed vesting of employee awards (in shares) 162,446 68,129 122,983 53,030
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) 53,987,555 53,769,379 53,932,804 53,733,521
Per share amount        
Basic EPS of Class A common stock (in dollars per share) $ 0.52 $ 0.32 $ 2.45 $ 2.21
Diluted EPS of Class A common stock (in dollars per share) $ 0.51 $ 0.31 $ 2.43 $ 2.19