Strengthening the lower back, most specifically the multifidus muscles (attached directly to the spine), supports the spine, engages when doing functional movements and also protects the inner organs. It is essential that it is relaxed but also strengthened.
The best way to strengthen this region, isn’t necessarily planks, but actually actively pushing your low back into the floor while on your back. This is a safe way to gently yet effectively begin to bring mind-body awareness to this area of the body as well as strengthen without rigorous, jolting exercises that may create more pain, discomfort and jarring of the spine.
Refer back to TVA engagement. When doing this engagement on the floor, as you push the air out of your lungs and rotate your hips, your low back begins to flatten on the floor which indirectly engages and strengthens the lower back/multifidus muscles to complete the 4th side of the inner unity “box” of core strengthening.
“The inner unit of the core consists of four major muscle groups that work as a system (see image above). The major inner unit muscles are the deep muscles running along the spine (multifidus), the muscles of the pelvic floor, the deepest abdominal muscle (transverse abdominus [TVA]), and the large breathing muscle (diaphragm). Two other muscles, the internal oblique and large latissimus dorsi, also play a part in inner unit function. The inner unit muscles are unique because they function together like a well-tuned crew of rowers. Their primary job with regard to movement is to stiffen the spine, rib cage and pelvic girdle so that the head, arms and legs have a stable working foundation.” (Chek, How to Eat, Move and Be Healthy, pg. 120)