What could cause lower back pain that is accompanied with pain shooting down the left leg and in the lower left abdomen area?

Many Things: Back injury back trauma twisting the back back muscle injury spinal disc disorder ligament injury too soft mattress too hard mattress.

Lumbar disc: Radiating leg pain is commonly caused by lumbar disc herniations. An upper level lumbar disc could cause pain in the lower left abdomen and down the anterior left leg. Other possibilities could be a muscle injury (likely hip flexor or abdominal muscle) or a hernia. It would be difficult to narrow down without more information.