The pro-remain campaign lied too and I would argue a great deal more. Take a look at the predictions of the immediate effect of Brexit vote (for 1017-18) on page 9 of the Treasury report: https://assets.publishing.service.gov.uk/media/5a80772140f0b...

This whole argument is why we do not have more direct democracy. The people in power and people who benefit from the status quo do not want the hoi polloi taking the "wrong" decisions. We might end up nationalising things or taxing big business effectively or all sorts of terrible things. Better to just give people the illusion of choice by letting them choose between two "neo-liberal" parties.