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Good Morning and welcome! I am Dr. Loretta, a licensed veterinarian and I am happy to answer your question.
The first question to ask your vet is if an injection was given in that back leg that is not working well. Sometimes, an injection can hit the sciatic nerve and cause a temporary paralysis in that leg which will resolve within a few days to a week. The fact that Lolly is so young and there is no feeling of pain in that leg that she is favoring tells me that this may be the problem. Arthritis is extremely rare in such a young cat and if they took xrays, if there was something wrong, it would have shown up unless there was a cruciate tear. This is the ACL or Anterior Cruciate Ligament that can rupture and cause lameness in the leg affected. Your vet can test this on physical exam but even this is unusual.
Take Lolly back to your vet and ask these questions. This all seems very odd to me.Does that make sense to you?
Please let me know if you have ANY other questions. My goal is to give you 100% satisfaction and if you are not yet satisfied, please REPLY so I can clarify for you.Sincerely, ***** *****