biking with lower back pain
Others have mentioned good tips about position, but I thought I'd add a few things other than that which I find helpful to reduce lower back pain:


I stopped carrying any sort of bag on my back (no matter how seemingly light!) and switched a rack with panniers
I stretch after riding, focusing particularly on my lower back (obviously), but also my buttocks and hamstrings, since having these tight can lead to lower back pain.
When I'm getting back into commuting after not riding for a while, I give myself more recovery time between rides to gain strength. In other words, don't start from zero biking days to biking every day and expect to not be in pain.


I've found that these steps have largely eliminated the problem for me.