He can’t be fired because he owns a majority of the company.
83% of independent Facebook investors believe Mark Zuckerberg should be fired as chairman of the board.
It is extremely rare for a majority of common stockholders to vote against their own CEO with such a massive majority.
The shareholders’ problem is that Zuckerberg has a history of making mistakes.
Source: Mark Zuckerberg: A single point of failure at Facebook, a company that is systemically important to the internet – Business Insider
He can continue to lie at will and nothing can be done, short of more users returning to reality and deleting their Facebook content and accounts.