Technically, though, I believe a lumi's head already qualifies as severed. They're meant to be severed, but they're still severed.
So I think applying the template would result in a lumi who instantly falls over, constantly regenerating and popping off heads until someone takes misery on it and sets fire to the comatose body.
Alternatively, since the template explicitly lets you attack the neck (which you can't on normal creatures), the lumi either grows a new couple of necks, or you can just stab it in the neck that isn't there.