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Note 11 - Equity Compensation (Details Textual) - USD ($)
$ / shares in Units, $ in Millions
1 Months Ended 3 Months Ended
Nov. 30, 2022
Sep. 30, 2024
Sep. 30, 2023
Nov. 30, 2021
Share-Based Payment Arrangement, Expense   $ 1.1 $ 1.2  
LSi Employee Stock Purchase Plan (ESPP) [Member]        
Employee Stock Ownership Plan (ESOP), Number of Allocated Shares   239,000   270,000
Employee Stock Ownership Plan (ESOP), Discount Percentage       10.00%
Employee Stock Ownership Plan (ESOP), Shares Contributed to ESOP   3,000    
Restricted Stock Units (RSUs) [Member]        
Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Grants in Period   107,217    
Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Grants in Period, Weighted Average Grant Date Fair Value   $ 14.92    
Performance Shares [Member]        
Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Grants in Period   160,826    
Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Grants in Period, Weighted Average Grant Date Fair Value   $ 14.92    
The 2019 Omnibus Award Plan [Member]        
Share-Based Compensation Arrangement by Share-Based Payment Award, Number of Additional Shares Authorized 2,350,000      
Share-Based Compensation Arrangement by Share-Based Payment Award, Number of Shares Available for Grant   1,438,315    
The 2019 Omnibus Award Plan [Member] | Restricted Stock Units (RSUs) [Member]        
Share-Based Compensation Arrangement by Share-Based Payment Award, Award Vesting Period   3 years