Stock-based Compensation and Equity Grants - Stock-based Compensation Expense (Details) - USD ($) $ in Thousands	3 Months Ended		6 Months Ended
	Mar. 31, 2022	Mar. 31, 2021	Mar. 31, 2022	Mar. 31, 2021
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total unrecognized expense	$ 6,306		$ 6,306
DLH employees
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total unrecognized expense	5,982		$ 5,982
Weighted average share based compensation expense recognition period			4 years 4 months 20 days
Non-employee directors
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total unrecognized expense	324		$ 324
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)			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)			161,485
Selling, General and Administrative Expenses
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total stock option expense	809	$ 386	$ 1,309	$ 844
Selling, General and Administrative Expenses | DLH employees
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total stock option expense	647	270	985	612
Selling, General and Administrative Expenses | Non-employee directors
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total stock option expense	$ 162	$ 116	$ 324	$ 232