There are two primary reasons for cats to excessively groom or barber, where they leave themselves bald or with only light hair coverage. The most common is an allergic type condition that causes the skin to itch or tingle and the excessive grooming is a response to trying to allieviate the itch. We see this as part of a syndrome called eosinophillic granuloma complex. Some cats will actually get thickened plaques that are licked raw and represent an inflammatory response in the skin similar to hives. Rather than being circular like most hives, these plaques, if they are visible, tend to be linear in nature. If this is the case, an injection of methylprednisolone will often resolve the problem and provde relief for 4-6 weeks. Some cats have a very focal season that they seem to barber while others seem to be repeat customers, dealing with this all year round. This may represent a food allergy or an environmental allergen that is not seasonal (house dust mites, carpet fibers, etc... are year round in many homes). Oral antiinflammatories can also be used to treat/diagnose the condition. If there are plaques, consideration of biopsy should be discussed, to ensure there isn't tumor. More often than not, response to therapy can be a reasonable way to make a directed guess of the condition.
Cat's that don't respond to steroids may have a different condition called psychogenic allopecia. This is a behavior vice, similar to chewing ones fingernails or cribbing in horses. This often responds to behavioral modifying drugs such as amitryptilline (elavil).
I think a reasonable thing to do if this seems fairly symmetrical, and there are no obvious wounds or growths/tumors stimulating the attention is to provide your Lilly with some antiinflammatory from the vet and then guage the response as an effective tool to not only hopefully treat, but get an answer. If there are thickened plaques that arise, bioposy or impression smears looking for eosinophils can provide the answer. Hope this helps.