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Stock-Based Compensation and Equity Grants - Stock-based Compensation Expense (Details) - USD ($) $ in Thousands | 3 Months Ended | 6 Months Ended
--- | --- | ---
Mar. 31, 2024 | Mar. 31, 2023 | Mar. 31, 2024 | Mar. 31, 2023
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items] |  |  |  |
Total stock option expense | $ 954 | $ 800 | $ 1,573 | $ 1,352
Total unrecognized expense | 7,385 | 8,934 | $ 7,385 | $ 8,934
Restricted Stock Units |  |  |  |
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items] |  |  |  |
Number of restricted stock units granted (in shares) |  |  | 429,320 | 337,578
Expected term (years) |  |  | 3 years |
DLH employees |  |  |  |
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items] |  |  |  |
Total unrecognized expense | 7,026 | 8,575 | $ 7,026 | $ 8,575
Weighted average share based compensation expense recognition period |  |  | 3 years 3 months 14 days |
Non-employee directors |  |  |  |
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items] |  |  |  |
Total unrecognized expense | $ 359 | $ 359 | $ 359 | 359
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 | 50,367 |  |
NEO | Restricted Stock Units |  |  |  |
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items] |  |  |  |
Number of restricted stock units granted (in shares) | 0 |  | 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 | $ 774 | $ 621 | $ 1,314 | 993
Selling, General and Administrative Expenses | Non-employee directors |  |  |  |
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items] |  |  |  |
Total stock option expense | $ 180 | $ 179 | $ 259 | $ 359

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