I'm hoping it is just a fat deposit or a cyst. The vet will probably do a fine needle aspiration and have a look at what he draws out under the microscope. I've had a few cats have FNA's and they have never required local anesthesia or anything and it just takes a few seconds to get a sample of what is in the lump. If it is a fat deposit or a cyst, the vet can usually tell right away. If they are unsure, they will send it off for further testing. How big are the lumps?
Good thoughts and prayers headed your way.