Parents have a 12yo lab that started limping. Took her to the vet, left leg was swollen and she had a fever. Xrays showed nothing wrong with bones or joints. Gave her antibiotics and pain meds. She was getting better then got a lot worse. Took her back yesterday. The swelling has spread, whole rear leg is swollen. Still running a fever. More antibiotics and a antibiotic shot.

What could be causing this? Lyme disease test was met, no signs of bites or cuts.

Sounds like they have ruled out most issues.  I would be thinking a soft tissue injury or cruciate injury but without seeing the dog, that's the best I can do.  With the age of the dog I would also be concerned about cancer,  unfortunately in an old dog, it's a common occurrence.

Cschelk2 DVM