The sooner that you deal with breaking up, the better for both of you. Sometimes it's better to set a boundary and not have any contact. I'm not a big fan of lying ; I think it's bad karma. Maybe it's something else. Lie about who cleaned your place.
If you deceive him either by lying or knowingly allowing him to have the wrong impression, then you become a bad person.
Should You Tell Him You're Seeing Someone Else?
OKAY, okay, calm down! The sooner that you deal with breaking up, the better for both of you. Every interaction with him is driving you absolutely insane, and you're not sure if you're totally done with him, but you are sure you need a break from this emotional roller coaster. Now, which of these responses is the problem, again? He is entitled to know whether he's in an exclusive relationship or not, and I don't think you have the right to be irritated.