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Note 9 - Equity Compensation (Details Textual) - USD ($)
12 Months Ended
Jun. 30, 2023
Jun. 30, 2022
Nov. 30, 2021
Nov. 30, 2019
Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Grants in Period, Gross 0      
Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Exercises in Period, Intrinsic Value $ 2,000,000.0      
Proceeds from Stock Options Exercised 3,862,000 $ 26,000    
Reduction of Federal Income Taxes Payable Related To Stock Option Exercise 800,000 200,000    
Reduction of Deferred Tax Asset Related to Stock Option Exercises $ 100,000 $ 100,000    
Share-Based Compensation Arrangement by Share-Based Payment Award, Shares Issued in Period 43,722 42,420    
Shares Issued, Value, Share-Based Payment Arrangement, before Forfeiture $ 400,000      
Deferred Compensation Arrangement with Individual, Shares Issued 207,090 494,047    
Deferred Compensation Plan With Rabbit Trust [Member]        
Treasury Stock, Common, Shares 922,426 821,876    
Treasury Stock, Value $ 7,200,000 $ 5,900,000    
LSi Employee Stock Purchase Plan (ESPP) [Member]        
Employee Stock Ownership Plan (ESOP), Number of Allocated Shares 256,000   270,000  
Employee Stock Ownership Plan (ESOP), Discount Percentage     10.00%  
Employee Stock Ownership Plan (ESOP), Shares Contributed to ESOP 14,000      
Restricted Stock Units (RSUs) [Member]        
Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Grants in Period, Gross 197,915      
Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Grants in Period   146,821    
Share-Based Payment Arrangement, Expense $ 1,300,000 $ 900,000    
Share-Based Payment Arrangement, Nonvested Award, Cost Not yet Recognized, Amount $ 1,100,000      
Share-Based Payment Arrangement, Nonvested Award, Cost Not yet Recognized, Period for Recognition 1 year 7 months 6 days      
Dividends $ 101,931 $ 65,743    
Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Vested in Period, Fair Value $ 800,000      
Performance Stock Units [Member]        
Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Grants in Period, Gross 190,510      
Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Grants in Period 190,510 190,980    
Share-Based Payment Arrangement, Expense $ 2,000,000.0 $ 1,600,000    
Share-Based Payment Arrangement, Nonvested Award, Cost Not yet Recognized, Amount $ 1,200,000      
Share-Based Payment Arrangement, Nonvested Award, Cost Not yet Recognized, Period for Recognition 2 years      
Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Grants in Period, Weighted Average Grant Date Fair Value $ 6.90      
Service-based Options [Member]        
Share-Based Compensation Arrangement by Share-Based Payment Award, Award Vesting Period 3 years      
Share-Based Payment Arrangement, Option [Member]        
Share-Based Payment Arrangement, Expense $ 300,000 $ 700,000    
Share-Based Payment Arrangement, Nonvested Award, Cost Not yet Recognized, Amount $ 100,000      
Share-Based Payment Arrangement, Nonvested Award, Cost Not yet Recognized, Period for Recognition 2 months 12 days      
The 2019 Omnibus Award Plan [Member]        
Share-Based Compensation Arrangement by Share-Based Payment Award, Number of Shares Authorized       2,650,000
Share-Based Compensation Arrangement by Share-Based Payment Award, Number of Shares Available for Grant 2,417,793      
The 2019 Omnibus Award Plan [Member] | Restricted Stock Units (RSUs) [Member]        
Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Grants in Period 197,915      
Share-Based Compensation Arrangement by Share-Based Payment Award, Award Vesting Period 3 years      
Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Grants in Period, Weighted Average Grant Date Fair Value $ 6.9      
The 2019 Omnibus Award Plan [Member] | Performance Stock Units [Member]        
Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Grants in Period 190,510      
Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Grants in Period, Weighted Average Grant Date Fair Value $ 6.9