Before you start training the client, find out for sure which lumbar vertebrae have been fused.
In your post you put L3-L6. FYI, there are only 5 lumbar vertebrae.
After you find out, I believe it is important for you to understand the function of the entire vertebral column, but more so the limitations your client will have as a consequence of spinal fusion.
Too, don’t forget the muscles that originate and attach on the lumbar spine. You will have to take this into consideration when designing the program for your client.
I hope this gives you a bit of direction.