Man arrested in Louisville Arby's after refusing to cover gun, police say

Felons - federal law prohibition so of course Kentucky law doesn't mention it

Mental illness - only if involuntarily adjudicated, and only with respect to trying to buy from dealer - again, federal

DV - only if CONVICTED of DV assault - again federal. But having a DVO doesn't necessarily remove your right to carry, only if convicted of DV assault. (I think eventually that one will go to court in Kentucky somewhere.)

And best I can tell, no prohibition on someone with dishonorable discharge, either.