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Stock-Based Compensation and Equity Grants - Stock-based Compensation Expense (Details) - USD ($) $ in Thousands | 3 Months Ended
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Dec. 31, 2023 | Dec. 31, 2022
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items] |  |
Total stock option expense | $ 620 | $ 552
Total unrecognized expense | $ 8,522 | $ 5,288
Restricted Stock Units |  |
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items] |  |
Number of restricted stock units granted (in shares) | 367,795 | 140,404
Expected term (years) | 3 years |
DLH employees |  |
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items] |  |
Total unrecognized expense | $ 7,983 | $ 4,750
Weighted average share based compensation expense recognition period | 3 years 5 months 1 day |
Non-employee directors |  |
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items] |  |
Total unrecognized expense | $ 539 | $ 538
Non-employee directors | Restricted Stock Units |  |
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items] |  |
Number of restricted stock units granted (in shares) | 61,525 | 53,510
NEO | Restricted Stock Units |  |
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items] |  |
Number of restricted stock units granted (in shares) | 169,544 |
NEO | Performance Shares |  |
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items] |  |
Number of restricted stock units granted (in shares) | 84,773 |
NEO | Service Based Restricted Stock Units |  |
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items] |  |
Number of restricted stock units granted (in shares) | 84,771 |
Selling, General and Administrative Expenses | DLH employees |  |
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items] |  |
Total stock option expense | $ 540 | $ 372
Selling, General and Administrative Expenses | Non-employee directors |  |
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items] |  |
Total stock option expense | $ 80 | $ 180

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