Can straining during bowel movements cause ongoing lower back pain?

Yes. Straining with bowel movements can increase you intrabdominal pressure which can exacerbate back pain and can also worsen pain that may be resulting from a disc herniation. Talk with you pcp about your issue. They may recommend a stool softener or even a laxative to help alleviate the bowel issues. They can also help determine if there is some other source to your back pain.