I am going to hijack your thread a bit, I have a similar issue also with left side of lower back. It doesn't hurt while walking/running or living everyday life. It does however hurt while bearing loads, say military press, squat, deadlift. Worst one is probably Good Morning. The pain isn't bad, but I can feel it when I do a good morning without any load, however taking in air and bracing my abs makes the pain go away while doing unloaded good morning movement.
I didn't injur it per se, it's just something that has creeped in over time I guess. I have been staying away from heavy movements for several weeks now, since I thought it was just some damaged tissue or inflammation, but it just doesn't go away! I can squat through the slight discomfort easily, but I am afraid I'd make matters worse.
What could be wrong?