I have (and had) lower back issues.
The only thing that fixes it are regular sets of sit-ups and hamstring stretches.
If you've got the money I'd spring for an adjustable air mattress (they're called "Sleep Number" or "Select Comfort" beds in the US). We've had one for 5 years now and it's great. All of my friends/colleagues with back pain purchased them after the pain started and many have no more back pain. I'm just a satisfied customer, not a pimp.
If you don't and still decide on the futon, I concur about the spring mattresses. Get a
solid wood frame, too. My wife and I have already broken an inferior wood-framed one.