Can lumbar tap pain last a few months?

Yes: The pain can arise from several causes: blood in the muscle along the needle path, blood under the ligamnet pierced to do the tap correctly, local inflammation around the sac tapped, and a small collection of the fluid, that can always leak a bit from the puncture site. If worse when up, and relieved when flat abed, it is worth mentioning to the person who performed the tap.

Not usually: Spinal tap discomfort usually only lasts up to a day or two. If pain persists for months it may indicate that a bleeding occured along the needle tract or that a nerve root got irritated.