I've dealt with lumbar back pain for a few years on and off, I think the lumbar region is the most common area of the back for pain.
the lumbar region is sometimes referred to as the lower spine
Yes that is correct, and the middle back is usually called the thoracic region, while the neck area is called the cervical region.
 A lumbar strain is a stretch injury to the ligaments, tendons, and/or muscles of the low back. 
I've definitely had lumbar strains before, as many Americans have I think, almost nine out of ten adults have back pain at some point in their life.