Lower back pain often indicates that the spine is not straight down there. This is not definitive, but it's worked for me and for others who have tried it. Sit on your bike with a straight back. Don't slouch.

This change in position can help you do that. Move the saddle back on the rails, say a centimeter or two (and lower it a little less if necessary). This gives the lower back a little more room to stretch out and moves your center of gravity away from the handlebar.

Some riders just slouch out of habit and some slouch because it seems to solve a balance problem. Either way, it's bad for your back.