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.
The specificity required of legislation to enact such a thing would be ridiculously un-tiny.
But, yes, it should be done, it should exist, it is the right thing to do, it is worth the effort.