Stock-based Compensation and Equity Grants - Stock-based Compensation Expense (Details) - USD ($) $ in Thousands	3 Months Ended	12 Months Ended
	Dec. 31, 2020	Sep. 30, 2021	Sep. 30, 2020
Selling, General and Administrative Expenses
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total compensation expense		$ 1,660	$ 910
DLH employees
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Unrecognized expense for DLH employees		$ 4,468	2,633
Weighted average period for recognition of compensation expense		4 years 8 months 12 days
DLH employees | Selling, General and Administrative Expenses
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total compensation expense		$ 1,193	563
Non-employee directors | Restricted Stock Units
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Number of restricted stock units issued (in shares)	63,177
Number of restricted stocks vested in period (in shares)		63,177
Non-employee directors | Selling, General and Administrative Expenses
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total compensation expense		$ 467	$ 347
NEO | Restricted Stock Units
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Number of restricted stock units issued (in shares)		147,431
Number of restricted stock outstanding (in shares)		147,431