Some background.
This is overall imprecise. Nothing is referred by "everyone" in other texts of rules and cards.CRF, Turn Sequence, Untap Phase wrote:Corruption checks triggered at the end of the untap phase happen after everyone
untaps.
Not sure whether "everyone" refer to every character, or to every card.
But regardless of resolution of the question, other question remains:
what if in untap phase no card has been untapped?
Is corruption check from Lure of Senses not triggered in such situation?
There would not be an end of the untap phase?
If trigger is set on end of actual operations of untapping, then yes.
A solution may be setting the trigger on a time in which all potential untap operations should be completed.
And this is idea behind variant (c).
"If at a Haven during his untap phase, a character with this card may attempt to remove it (but not untap or heal)."
specifies site and time at/in which the character may potentially untap/heal. Whether the character is actually able to perform untap/heal is not checked (may be untapped, tapped and control Dreams of Lore etc.) .
This means that after the attempt, a time which the character may potentially untap/heal passes. So the character cannot untap/heal. or make next attempt to remove that or another copy of Morgul-knife.