Since no one has chimed in,
If you have been cleared to lift weights:
Compression is your enemy. Find a way to decompress the low back every workout. Realize that if you continue to lift heavy, the disc may move out further and pinch the nerve. I have canal stenosis now and it sucks.
As far as core goes, I do a lot of ab wheel work, QL exercises, various low back exercises, including GHR, reverse hypers, hypers, and a lot of glute work. Most will tell you to stay away from twisting movements, but I do woodchops with no problems. I do not recommend side bends.