By tradition, if he’s lied to parliament, he should resign. What are the chances of that? Then the opposition could call a vote of no confidence which they would lose because they don’t have the numbers. Then the 1922 committee could get the numbers to sack him, which they won’t because no-one wants a leadership contest dragging on for months….
So he’ll sack a few people from number 10, announce a few Tory policies for the back benchers to take back to the local parties and stay put.