Stock-Based Compensation and Equity Grants - Stock-based Compensation Expense (Details) - USD ($) $ in Thousands	3 Months Ended		6 Months Ended
	Mar. 31, 2025	Mar. 31, 2024	Mar. 31, 2025	Mar. 31, 2024
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total stock option expense	$ 533	$ 954	$ 725	$ 1,573
Restricted Stock Units
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Number of restricted stock units issued and outstanding (in shares)	697,384	429,320	697,384	429,320
Selling, General and Administrative Expenses | DLH employees
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total stock option expense	$ 403	$ 774	$ 416	$ 1,314
Selling, General and Administrative Expenses | Non-employee directors
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total stock option expense	$ 130	$ 180	$ 309	$ 259