What is important is the number of votes cast by either side and if the outcome is unacceptable to some then why bother with the referendum in the first course
We ought not to have had the referendum. I agree with that and Cameron only had it because he was terrified Farage might herald a lot of Tory MPs leaving to join UKIP.
But I've never considered the simplistic notion that it's only the number of votes that counts to be valid; where major decisions of the magnitude of this are taken then it has to be demonstrably the will of the majority of the electorate, not simply those who voted. Otherwise, you're allowing a minority to dictate the future for the majority, and there's no way that can be described as democratic.
There's also the feedback which suggested a lot who voted leave did so because they disliked Cameron - a worrying motive in itself, but certainly not a justifiable foundation for the outcome.
In terms of lies, whom should we hold responsible when the NHS collapses through lack of funds? Because the Leave campaign convinced a lot that £350m was what it cost per month to stay in the EU - the biggest lie of all.
Politicians don't all lie; I know some (Tory, in fact) personally and they're very open and honest. They're just not the ones who make the headlines.