I had back surgery(L4/L5) three years ago and struggled to get back into running. I kept getting pains in my butt and right leg and had to stop running. I saw my surgeon and he said I had to work on my core muscles. I did so with vigor but I had the same problems. About a year ago I decided if I couldn't run I would strengthen my upper body so I started doing pushups. I got up to over 1000 per week-unfortunately I developed shoulder problems but(runners never do anything in moderation) but when I started running six months ago I was able to do so pain free.
Abs are really critical to running well, but be careful not to over-strengthen them. Tight abs are a frequent cause of lower back pain in the vicinity of the erector spinae muscles, regardless of the condition of the spine itself, and can increase pressure on the spinal disks by pulling downward on the ribs. Make sure to keep them free of trigger points, and flexible with safe backward stretches on a Theraball or equivalent.