you are not lying -- you are omitting something not required by law to disclose and against the law to be asked about. that is not lying. they can't ask about mental health (or at least you don't have to answer). never say you have a disability on those job applications. ever. there is no reason to. if you can say you are adequately capable with "reasonable accommodations" then that is all they need to know. at the interview you can discuss those reasonable accommodations.

right now, in this point in time, you are shooting yourself in the butt to say anything about mental ANYTHING. the mindset is "show no weakness."