Possible neuropathy. Pain described as burning is often a sign of neuropathy, a functional disturbance or pathologic change in a peripheral nerve. Causes include diseases like diabetes, excess alcohol intake and nerve entrapment as occurs with carpal tunnel syndrome. See your doctor or a neurologist for a proper evaluation.
Slipped disk. This pain could be a slipped disk in your lower back. A physical examination and and an MRI of your lower back can help to identify the problem. Other problems could be a circulation problem in your leg arteries. Check with your doctor or a neurologist.