Under what circumstances can my car fall under the lemon law?

I purchased a car with an extended warranty which I later found had many issues, from an actual dealership. Neither the dealer, nor the warranty company will compensate for my broken engine and transmission mounts, leaving me to have to cough up half of the car's price. Does this fall under the lemon law??

Thanks.
It's a full aftermarket warranty purchased from the dealer itself. The motor mounts gave shortly after I bought the car, 800 or so miles later, the test drive was fine!

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