Does this license automatically cover the Great Lakes or is sea time on the Great Lakes needed as well?
An endorsement only for Inland is not valid on the Great Lakes, see 46 CFR 11.430(b):
Any officer endorsement issued for service on inland waters self-propelled vessels, excluding towing vessels, is valid for the inland waters of the United States, excluding the Great Lakes.
You can get the endorsement for Mate AGT Great Lakes and Inland with inland time only, time on the Great Lakes isn;'t needed, see 46 CFR 11.437. The difference is what exam you take for the endorsement, inland only or Great Lakes and inland.