If I have above 80 lp, can the next win directly get me to promo?

That's just how the system works, and it would completely screw things up in high ELO. People in diamond (IIRC) win somewhere around 2-3 LP per game, so a 20 point jump like that would be huge. If you've got enough points to get put into promos it'll put you there, otherwise you're gonna have to win the one awkward one. C'est la vie.

It might be cool though if they allowed some of the points you would have gotten (say you gain 20 but only need 4) to carry over to your next division/tier, so in the previous case you would start the next tier with ~16 points. That could be worth considering.

this happens to me a lot too, a friend of mine just dodges games until he finds a team he thinks can win when they have 90+ lp since the next win will get them to series