The muscles of the lower back play a critical role in posture, weightlifting (the specific sport), and lifting weights (generally). They keep your torso erect, making them helpful during just about every physical activity that involves running, bearing a load, or jumping. A strong lower back makes back pain and back injury less likely and aids in sports performance of all kinds.
So yes, it's kind of a good idea to strengthen the lower back.
Side note for those experiencing back pain. Your spine is held upright by both the rectus abdominis (abdominals) and the erector spinae (lower back). They act in opposition, much like guy wires hold up a radio tower. If tension on one set of muscles is greater/less than the other, there will be stress on the spine. What can happen is that if the abdominals are weak, the lower back muscles will be pulling on the spine more than normal, causing strain in those muscles. So, counterintuitively, a sore lower back can possibly be due to weak abdominals.
Rather than work on the lower back specifically, I recommend working on your core instead. That involves the lower back, the abdominals, the muscles on the sides, etc.
Most people have postural problems related to pelvic tilt; either tilted forward (anterior) or tilted back (posterior). This can lead to lower back pain and problems if you start to lift more weight in squats or deadlifts.
If you work smart on your lower back not only will it slow down degenerative disc disease, but will be more trained for injuries.
Often people with sedentary work complaint from low back pain or cervical pain. Normal human spine position is straight. When you sit spine take more than 20% more from normal load. Every years catabolic processes destroy more and more cells in intervertebral discs (ivd). Micro traumas like sitting in with bad posture, bending and twist accelerate this process.
When training your low back, you help your muscles where support spine to be more strong and stick it in place. IVDs will get more reserved for long time.
Decreasing degenerative disc disease is complex process. You'll need not only train muscle on low back, but all back, gluteal muscles and legs. They take pressure from body weight when sitting. Exercises like dead lift and squats are great for good body form. I mean every free weight exercise is good choice.
Drink plenty of water not only help for back, but for all body parts.