I guess all public statements would essentially be “under oath” and would be held to that standard. So the questions would be 1) which statements are public and 2) what constitutes a lie.

It can be proven that someone has lied - for instance, if they have said something on the record previously that indicates they had foreknowledge that what they said was false. It’d be a large administrative burden, so I imagine that only consequential lies would be prosecuted. But the law would also be ripe for abuse - an opposing political faction could scrutinize everything a public official says, sue them for everything that wasn’t true, and tie them up with court appearances and fees for a long time.

Anyway, it’d be very difficult to consistently enforce this law and prevent it from being abused.