I have a lower back problem and was wondering if a lazy boy recliner would make it any worse?

Try before you buy. It depends on what is causing your back pain. Different back pain responds to different treatment. You need to "test drive' a friend's lazy boy and see if it helps or hurts. You might also consider trying out an inversion table to see if that helps. In other cases, trampolines are the ticket.
Probably not. Probably not. Try a friend's recliner or try one at the store for awhile. A friend or family member may be less likely to rush you; in the store you can nicely ask the salesperson to let you see how comfortable it is over a "reasonable period of time." you might be able to talk them into a money back trial. You might look into a furniture rental company for a trial. Try several models and brands.