Never been on Lyrica,but I find that the neurontin helps with the burning, buzzing, and zapping pain, not so much the deep soreness or the really bad pain in the late afternoon and evening. Most of us seem to be on ome other kind of painkiller for that breakthrough pain. For me it is the "I can't stand it anymore" or if I really have some work that has to be done. I take a low dose oxycodone, but I know the day is coming when I will need something stronger, or 24/7. My doctor has tried to move me to a butrans patch, but for now I prefer only taking something when I really need it, although I realize this strategy results in higher pain levels than are necessary.
My experience is that neurologists do not like to prescribe pain meds, and prefer your family doctor do so. You need more pain relief than you are getting. Ibuprofen is useless for nerve pain unless you also have arthritis.