I too am ravenous if I do serious lifting. I am probably a bit fatter than you. I don't really know what your goals are, but really the best thing to do is find a way to lift that you can still eat at a deficit. For me, I lift every day not even going close to failure. Basically I do a half set of a full body routine every day. It is enough to keep me from losing muscle (and possibly even gain as a beginner) but not enough to impact my hunger or leave me sore.
I find that if I get sore from lifting I can't eat enough. But if I avoid being sore but lifting a small amount every day I don't get hungry.