As with any exercise routine post injury or post therapy, it is ideal to get clearance from your dr or health service provider before continuing on with more strenuous activities.
Lower back injuries is one of the most common ones out there. We have all come across this at some point in our lives. Nothing is more important than rest, first and foremost. Depending on the severity, rest (and in some cases ICE) may repair areas without further action. If recovery time is longer than anticipated, make sure you see a health practitioner for further advice & clearance before exercising.
My advice, and I explain this to my clients, is to prioritize not necessarily the resistance when training, but focusing on your postural muscles during movement (ex erector spinae, lats, etc), which is mainly the lower back. Keep your head held high throughout the entire movement, with the chest upright. This will align & keep the back set at a correct postural positioning (see above):
Try not to bend the back too much. Refrain from any deadlifting, straight deadlifts, or anything involving hip flexion throughout the movement (ex squats, leg presses) or heavier weight that will cause exaggeration, or swinging movements.
Keep the weight light-to-moderate, about 10-15 repititions and a slight "squeeze" at the concentric portion of the movement, 3 sets. To begin, only start with 2 back exercises, increasing the exercises and/or sets the next time if you're able to manage.