I think to answer OP's question though, yeah, lower back pain is to be expected while on the bike, at least during hard efforts. Along with your legs, arms, shoulders, calves, and everything else.
But if you're cruising along at a casual pace, not out of breath or anything, and your back hurts in any way, that's not good and is a problem that will need to be studied a little, but should be able to be remedied by way of adjustments to yourself and to the bike.
This is assuming no previous lingering injuries or genetic back abnormalities.