Can inflamed gut cause lower back pain?

Yes,: Inflammed bowel can cause peritonitis or referred pain which may radiate to the back.

Yes: There are non-spinal origins of low back pain, and having abdominal inflammatory issues can relate with symptoms of back pain. Other non-spinal causes include aortic aneursym, kidney/ureteral issues, uterine fibroids, ovarian cysts, hip pathologies, and also prostate inflammation. If pain continues, seek out medical attention.