Stock-Based Compensation and Equity Grants - Stock-based Compensation Expense (Details) - USD ($) $ in Thousands	3 Months Ended		6 Months Ended
	Mar. 31, 2024	Mar. 31, 2023	Mar. 31, 2024	Mar. 31, 2023
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total stock option expense	$ 954	$ 800	$ 1,573	$ 1,352
Total unrecognized expense	7,385	8,934	$ 7,385	$ 8,934
Restricted Stock Units
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Number of restricted stock units granted (in shares)			429,320	337,578
Expected term (years)			3 years
DLH employees
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total unrecognized expense	7,026	8,575	$ 7,026	$ 8,575
Weighted average share based compensation expense recognition period			3 years 3 months 14 days
Non-employee directors
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total unrecognized expense	$ 359	$ 359	$ 359	359
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	50,367
NEO | Restricted Stock Units
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Number of restricted stock units granted (in shares)	0		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	$ 774	$ 621	$ 1,314	993
Selling, General and Administrative Expenses | Non-employee directors
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total stock option expense	$ 180	$ 179	$ 259	$ 359