2F - we're probably just saying the same thing in different ways, but I was taught a little differently on lunge form.
Rather than pushing off with the back
foot, I always heard that the back leg and foot are strictly for stabilization -- the front foot and leg are where your weight and power are. So you push through the heel of the front
foot and use the muscles of the front leg to get back to the starting position. Once I began focusing on pushing through the heel of my front foot, I discovered that I was stronger doing lunges.