I think this answer is very simple and that is he thought Hillary was easily poised to win the election so he didn’t want to muddy the waters. Trump had already said there was a possibility that he’d contest the election because of some nefarious things that were going on with voter rolls and of course it was Democrats who were involved.
They don’t admit it but all it takes is some internet research and you can see which Party is typically guilty of voter fraud; do you remember Acorn? Anyhow, Obama wanted to make sure it was a smooth election because his candidate was winning. The bottom line is there’s no question he lied to the American people.