It is possible, but unusual to "strain a muscle" in the lower back. I say this because the anatomy is more or less protective against overstretching muscle in that region, especially with movements into rotation. That is not to say that there is no muscle involvement LBP; instead, muscle guarding is typically more of a symptom of LBP rather than the cause. In back pain therapy, we go a long way toward dealing with the muscle guarding associated with LBP, but resolving the muscle guarding does not do much for the underlying pathology. That must be addressed separately in order to successfully treat LBP.