First of all, you are a very healthy weight and losing weight obviously hasn't helped your back so don't try to lose anymore, make sure you eat enough as it sounds like your gym regime is quite rigorous! here is an exercise I found just by googling "lower back fat"
Back lifts (strengthens your lower back):
Lie on your stomach with your palms resting on the floor near your shoulders and with your legs outstretched. Pull your abdominals in towards your spine as if you are trying to create a space between your belly button and the floor. Rest your forehead on the floor to align your neck with the rest of your spine.
Without using your hands, lift your head and chest up off the floor as high as you comfortably can. Your palms will lift a small way off the floor too. Hold a moment until you feel a stretch through your lower back and then slowly lower