Lumbar puncture is done by an injection in lower part of spinal cord and CSF is withdrawn for diagnostic purpose. In some cases spinal anesthesia is given after doing lumbar puncture. It has no side effect except low back pain. It does not harm any nerve.
Lumbar Punture is done in the L4 spine level. In Lumbar punture injections the medicine
gets mixed with the cerebrospinal fluid which is in the spinal cord and it goes to the
brain. For the purpuse of spinal anasthesia, lumbar punture is done. Also lumbar punture
is done for a type of Leukemia called ALL (Acute lymphoblastic Leukemia)
Unfortunately, it does happen. You should talk to your doctor about it especially if you are in pain or are having numbness in your legs. If the puncture was for a pain procedure, it could be related to that as well.
In a lumbar puncture the spinal needle is introduced into the subarachnoid space and the Cerebro spinal fluid is collected for further testing. During the process complications such as severe headace can arise. Nerve damage just during a lumbar puncture procedure is unlikely.