I play with the guitar on my left leg also even though I am right handed. My back will start getting stiff if I am sitting for long period of times. While you are playing make sure you have good posture. You should not be slouched over since this can cause back problems. Also one thing that has helped me is have a comfortable chair to practice in. This has allowed me to practice for longer periods of time and not feel discomfort in my back. These are some things that have helped me so they may be worth trying out.