What is the best course of action after failed back surgery (lumbar laminectomy). Persistent burning pain along outside of leg and back weakness.

Re-eval. You need to be re-evaluated, preferably by your surgeon. Alternatively, you could consider seeing a non-surgical spine specialist, usually a physiatrist. There may be more simple solutions to your pain.
Failed back syndrome. Failed back syndrome (FBS) can be caused by several different factors. Laminectomies, in particular, have been shown to result in spinal instability in biomechanical studies. Minimally invasive surgery (mis) can help obviate some of the complications associated with fbs. Medications like Neurontin (gabapentin) can also help with burning paresthesias. I would obtain a formal consult from a spine specialist.
Pain Management. Very few people make it long enough through the medical system to officially get a diagnosis of failed back syndrome. One back surgery does not necessarily do it, but 3-4 may.. You may need nsaids, muscle relaxers, neurontin, (gabapentin) antidepressants, narcotics, or combinations of these. As for your current condition, your fp or a pain specialist may be able to manage your pain issues from here, along w/ pt.