Stock-based Compensation and Equity Grants - Stock-based Compensation Expense (Details) - USD ($) $ in Thousands	3 Months Ended
	Dec. 31, 2022	Dec. 31, 2021
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total unrecognized expense	$ 5,288,000	$ 6,078
DLH employees (a)
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total unrecognized expense	$ 4,750	5,592
Weighted average share based compensation expense recognition period	3 years 8 months 12 days
Non-employee directors (b)
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total unrecognized expense	$ 538	$ 486
Non-employee directors (b) | Restricted Stock Units
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Number of restricted stock units granted (in shares)	58,517	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)	140,404	147,431
Selling, General and Administrative Expenses
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total stock option expense	$ 552	$ 500
Selling, General and Administrative Expenses | DLH employees (a)
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total stock option expense	372	338
Selling, General and Administrative Expenses | Non-employee directors (b)
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total stock option expense	$ 180	$ 162