I have struggled with a rubbish lower back for about a year now. I'm still walk/running back into running.
I did Reformer Pilates for 5 months (once a week on recommendation of physio), got a personal trainer who focused on my weak areas that were aggravating the lower back (core, glutes particularly) - although you could that yourself, and saw a physio/osteo every fortnight. Sorry if that sounds extreme but everytime I tried to get into exercise I just aggravated it back to square one again. It meant cutting back my cardio for a while as I def couldn't run, and cycling and rowing aggravated it.
If you really want a workout, try burpees, pressups, box jumps etc, tuck jumps if your back can handle it.
I think any professional would agree that for an injured lower back building up the muscles is crucial. Core core core (plank, side plank etc), glutes (one legged squats are good, and squats/lunges etc).
Yoga can be good - although when I was at my worst the physio told me my back wasn't ready for the back bends etc involved. I can now though, so maybe give it a try and see how it feels.
I really think that if can afford it, it's worth seeing someone to give you a diagnosis (if you haven't already) and an exercise programme.
Good luck.