In addition to lower back, make sure to work on your core altogether. Try bearcrawling, or crawling while in prone position.
Also, when you do do the actual PFT, rep out as many pushups as you can, maintaining good form, but just relying on the elasticity of your muscles by "bouncing."
But while you train, it helps to 'hold it'. Like go down, count to three, push up, count to three, and repeat. You'll burn out much faster (which helps), and tone your pectorals, deltoids and triceps better that way.