Earlier this week I had planned to go for a longish, hilly ride, but in the morning had moved a lot of heavy furniture from one home to another so my back was giving me a fair bit of pain.
I decided, with some trepidation, to go on the ride anyway. It was a bit uncomfortable for the first five miles, but after that there was no problem, even after some steep hills where I had to stand in the pedals.
No resulting after-effects, so I can attest to the benefits of cycling on lower back problems for me. YMMV.