I think a prohibition to lie to the public would already be incredibly impactful (if it had no statute of limitations and adequate punishments).
A delicate issue I see is how to handle personal matters that the public don't need to know.
Anyhow, you might think that it's hard to know when someone is really lying vs just being uninformed, but in truth in the long term most lies become apparent; while you couldn't prevent
every single lie, you'd reduce them enormously, in my opinion; even in countries where the president doesn't lie almost constantly.
If you think of any (societal) issue you care about, there's a good chance it would get solved with that tiny change