8 days ago I had a lumbar puncture and during the procedure I had a hot burning pain in the lateral thigh that radiated downward. Still on going?

Lumbar puncture pain. A pain (usually sharp) that radiates down the legs is suggestive of a nerve pain. I suggest you go back and discuss this issue with the health care provider who performed the lumbar puncture to make sure that these symptoms are not related to the procedure and that they need to be addressed.
Nerve root. Sounds like the L5 (5th lumbar) nerve root on that side was irritated when the needle brushed by it. There are medications that will relieve the symptoms (e.g. gabapentin, pregabalin, Cymbalta, (duloxetine) etc.) but the doctor who gives you the Rx will probably also tell you that you need to wait 1-3 months to see if it gets better on its own. Not much can be done for any nerve injury except give it time.
Call M.D. now. Definite call the physician who performed the LP- not a normal finding.