Oh my! Sorry to hear about poor Max.
General: Many times with an injury the affected limb will be noticably warm to the touch, and the dog may hold the limb out away from the body, resting or while mobile. I would check for heat in the leg and shoulder areas.
Lymes disease is detected through a simple blood test and can be done at your regular vets office in about 15 minutes. Lymes is tricky, false results are encountered often, and if he's ever been vaccinated for Lymes it may effect the test results.
Nerve damaged in humans results in numbness and some intermittant pain. Nerves can regenerate, again in humans it can take months. I can only assume dogs may have similar effects because we are all mammals.
Did LSU get any results back from anything they sent out on Max's spinal tap?
Dr Sisson's rates are quite affordable. He is expert in neurology, and has specialized in treating dogs with GME/NME, in addition to his normal caseload. He will do phone consults with you and your vet.
Another option may be to have Dr. Dodds evaluate his blood, also very reasonable.
I'll look up more info for you if you're considering anything I've mentioned.
Also, a video might be nice....
