I have noticed that he cuts the corner at the spot that I asked him to move out from me to start walking a circle (if that makes sense). Yes, he does it both directions. My main purpose in lunging is for when I don't have time to tack up and ride him, so he gets exercise in some way. I exercise him about 2-4 times a week. Not recently though, I've been cutting back on his exercise to help him gain weight for the winter.
I will admit, I think the reason why he's been cutting is because I didn't notice it when he was first learning to lunge, and when I did, I didn't think much of it. Every now and then, I would try to do something about it, like Skyseternalangel had suggested, but wasn't consistent with it. My goal now is to just get him to stop this habit, so I will be consistent.