Rinny Can fulfill Lust's deepest desire, simply ignore all her advances till you get the "Ask for??????" and you would be able to do this with all the Romancable NPCs.
As for the Island it is the Painting in the Upper New Ark, find a way to destroy the Statue, Simply sneak up behind the receptionist and then fiddle with the Statue, when time has passed the massive painting would have no one looking at it, Rest upon the Bench and the Painting of the Island would take you into itself.