Is there a Used Car Lemon Law if the car in question was bought at a well known dealership?

There is a used car lemon law in 6 or 7 states, but not in Kentucky. But Ky does have a Udap law and under that law in most states it is a violation of that law to sell a consumer a vehicle that is dangerous and unsafe for normal highway operation and that may work for your problem. The problem is here that you had your own mechanic look at the vehicle first; that makes it your mechanic's problem since they didn't discover this problem at the inspection they did for you. If you paid them for it then they would owe for the repair bill. If you didn't pay them for the inspection, then they may not. If you don't get this worked out, then you may want to think about filing a claim in your local small claims court for the repair cost or you should call your local attorney bar association and ask for a referral to a consumer law attorney near you.