Muscle imbalances can cause lower back pain in runners
During the late propulsive stage of running (also called the take off stage) there is tension created in the psoas and ilacus muscle as well the rectus femoris muscle, your hip flexors located in the front of your hip and groin.
These muscles also help to extend the lumbar spine and tilt the pelvis forward. To protect against these potentially injurious motions, the external obliques, and the rectus abdominus (2 of your important abdominal muscles which help with core strenght) pulls the pelvis upwardly counteracting forces caused by the hip flexors and allowing the spine and pelvis to function as a stable anchor.
So if your hip flexors are tight and over-developed this anterior or forward tilt of your pelvis can cause lower back pain.
To counteract this you must stretch your hip flexors and strengthen the abdominal muscles. This will reduce pelvic tilt and decrease the chance for low back pain to develop. Also, strengthening the low back can improve the balance between the muscles of the hip region.