I am sorry to learn that you are have back pain that is getting chronic. If you haven't already do get your doctor to assess this for you and review what the options are that might help.
Chronic back pain is quite common in the general population, so it doesn't have to have anything to do with your past medical history. I can't find any evidence to say that having lumbar punctures causes back pain in later life so I don't think this is related.
I did find a research paper about back pain in survivors of childhood acute lymphoblastic leukaemia (ALL), the most common type of leukaemia in childhood. This research found that back pain seemed to be more frequent in adult survivors of childhood ALL than it was in their unaffected brothers and sisters, so there could be a link, but then again there may not be.
I think it would be a good idea to ask your doctor too when you see them to get their input. I hope something can be done to improve the pain.
