I have had many. Nothing to worry about at all. Not too different than the epidural most women get before delivering a baby.
Biggest risk that I know of, which I understand not to be even dangerous is that removing even a small amount of spinal fluid (or a consequential leak from the puncture) can cause a bad headache for a few days afterwards. If it doesn't resolve on it's own, they just draw blood from your arm and re-inject it into your spinal canal. It's called a blood patch and works almost immediately
What type of doctor is doing it? A Radiologist or a Neurologist?
Hope whatever is going on is OK!