Yes, I had this problem for about six weeks this spring. I work as a roofer which is very taxing on the lower back.
It felt like the vertebrae just above my pelvis were cracked and some( nearly all) movements caused spasms in the lower back muscles.
I basically toughed it out and actually ran a pb for a half(stagnant for 5 years) when I could hardly stride out at all. Very strange.
If running doesn't make it worse I would keep going and just try to avoid the movements that aggravate it.
The back is one part of your body that evidence seems to indicate is best worked through when problems arise.
I did lots of hanging from a bar or ladder rung constantly through this period to try to get everything stretched out. Otherwise it felt like my lower back was going to disintegrate.
No problems since then and my back feels great today. I am a big believer that the body will heal in time if you keep moving.