Stock-Based Compensation and Equity Grants - Stock-based Compensation Expense (Details) - USD ($) $ in Thousands	3 Months Ended
	Dec. 31, 2023	Dec. 31, 2022
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total stock option expense	$ 620	$ 552
Total unrecognized expense	$ 8,522	$ 5,288
Restricted Stock Units
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Number of restricted stock units granted (in shares)	367,795	140,404
Expected term (years)	3 years
DLH employees
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total unrecognized expense	$ 7,983	$ 4,750
Weighted average share based compensation expense recognition period	3 years 5 months 1 day
Non-employee directors
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total unrecognized expense	$ 539	$ 538
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	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)	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	$ 540	$ 372
Selling, General and Administrative Expenses | Non-employee directors
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total stock option expense	$ 80	$ 180