Is it normal during a lumbar puncture to feel a zap or jolt down one leg or on one side as they are moving the needle inside?

"Normal"? Having an LP isn't "normal;" it's done to rule in or out an ABnormality. Do the symptoms you report occasionally happen during an LP? Yes. The needle may brush past and stimulate a nerve root. You feel the sensation in the body part from which the nerve root transmits sensory input to the brain. I suppose rarely the needle injures the root but I've never had that happen.