Upper body wise, my training is identical. Lower body wise, small changes. I no longer do heavy squats or deadlifts. I will do a few sets of 20 reps with lighter loads at the end of a work out. I tend to rely on leg presses, lunges, bulgarian lunges and goblet squats. Also have been doing lots of prowler pushing and pulling now. That cuases me no issues whatsoever.
My recommendation is to take things very slow as to avoid re injuring the area. Progress slowly and if youre ever unsure if you'll be ok with a movement, don't do it. It took about 5 months before I felt comfortable even doing leg presses. If youre training more for bodybuiling as oppose to powerlifting, then squats and deadlifts can easily be discarded at least for the time being.
There are plenty of alternatives such as the ones I listed above, and many more that dont require spinal loading. On bench, I started with my feet on the bench to avoid to much extension in the spine and slowly moved to putting plates under my feet and finally back to normal benching. Also avoid bent over rows, use chest supported for now.
Again I would stress core stability work and stretching to fix the underlying issues. For me it was tight hip flexors that causes unusual pulling on the lower back. It is a shitty thing to have happen, and from everyone I've talked to you will experience issues in the future, such as sciatica and soreness that will last for a week or two once in a while. We all have set backs, its how we respond to them that matters.
Stay positive and do youre rehab/prehab and things will work out for you. If you have any other questions feel free to ask. Glad I could help.