Yep. Completing that lower is manufacturing a firearm. That is legal, with no paperwork required, under federal law (as long as the result is not a machinegun or other NFA firearm) but with some states now banning "assault rifles" it might be illegal under state or local law.
Under federal law, note that if you manufacture a firearm for your own use, you must do all the work; you can't hire a gunsmith or a machinist to help you or to do it for you unless he has a manufacturer's FFL.
I have known several folks who bought those 80% receivers, both 1911 pistol frames and AR lowers, and only one was able to turn out a usable 1911 frame; the others either gave up or ruined the frame, or both.