No, Trump dislikes incompetence. Lying is okay as long as you're competent at it. Cruz being born in Canada is a real problem that hasn't been addressed. Don't think Trump is going to touch Cruz with a 10' poll and this is probably a Trump psyops to pressure Kasich into VP. For the good of the Party though, Trump needs to pick somebody young enough to be able to mount a legitimate campaign in 2024 and ideologically similar and not end up like Dan Quayle.
Possibly...Mary Fallin, Republican Governor of Oklahoma.