The whole concept of democracy has some serious flaws, which are being exploited mercilessly these days. (It is still probably just about the least bad of the possible political systems, but we probably need for there to be consequences for intentionally attempting to break the system for political advantage. Also, I don't think politicians lying should fall in the category of "free speech").
The idea that you might be able to ban lies in public life is predicated, consciously or unconsciously, on there being some kind of benevolent proactive God who can look down and tell humanity what is right. The need for a truly independent arbiter, which doesn't exist in the real world, is the key reason so many ideas for running a society fail. Systems that work reasonably well are the ones that have some amount of self correction inherent in them. They can still go off the rails, but less often.
Some lies are so obvious and blatant, they should be incontrovertible. However, in tribal societies people can't even agree what "woman" means any more.
You're confusing
opinion, for which one
would need an independent arbiter if one was insistent on assigning a truth value to an opinion, with
fact. Facts are verifiable, opinions are not. Whether someone has two X chromosomes and is therefore biologically female is a fact and is relatively easily proven one way or another, whether someone belongs to the gender set assigned the label "woman" is a social construct and therefore a matter of opinion or convention.
One does not actually need any fancy philosophy or to delve into the depths of epistemology to know the difference between truth and a lie. Most of us learned the difference at our mother's knee and any attempt to argue that it's difficult, with all the facts available, to distinguish a lie from an opinion or a bit of rhetoric is mere sophistry. Lying is when one deliberately presents something as the truth while knowing or believing it to be untrue, or when one presents something that is in itself strictly true while deliberately withholding information that one knows would invalidate the sense of what one is claiming or implying to be true (the lawyer's lie).
I think you were really trying to head in the direction of "doing the right thing" which is much broader than mere lying, that indeed does need an independent arbiter and in society we have assigned that rôle to "the rule of law". That lies and other misbehaviour in public life are not effectively punished is one of the the most corrosive things in society today. If Dominic Cummings can be a scofflaw with impunity why should anybody else obey the rules?