P.W.
Is this a tummy tuck with only local anesthesia? That sounds nuts. Why do you want to do that? If you want a tummy tuck, you will want general anesthesia. A tummy tuck is pretty major, you don't want to be awake for it. Don't worry, you won't die while you're under.
While a tummy tuck involves lipo, a tummy tuck and lipo are two different things. A tummy tuck involves excising (cutting off) loose skin and tightening muscles, lipo only involves sucking out fat.