I see the whole mess being because Cameron framed the referendum as non binding. He created the poisoned chalice.
I can see this working in one way. They can allow the vote and make it a vote of confidence. If the government wins it, then they trigger A50. If they lose it, then there is an election, the Tories campaign on broken trust, the other parties get massacred and they come back and trigger A50 claiming that it was a manifesto promise and the people had a direct and binding vote on it. They could allow Tory MP's a free vote on it too. How could she lose?
Making the vote to trigger A50 a vote of confidence puts the whole situation into an entirely new light. Because those who want to remain but know their voters will massacre them at the polls, are left with the stark reality that voting against triggering A50, should they be successful, will put them right in front of the voters within weeks. When feelings are at mutinous point.
It could be useful for the government to state that before it goes to the Supreme court where the judges will have to factor in what will happen to the political situation if they go against the voters and try to give the decision to the MP's even though the Public have, Democratically, Spoken.
If it does go to a vote in parliament, what could the Lords do to change it? Demand that parliament gets a vote on the terms? That's been offered already and would be accepted immediately. All it could do is force a delay of two or three months. Enraging the EU who are becoming more and more destabilised by the month whilst the UK goes from strength to strength.
Even if the Lords demand that the Parliament has a vote on the terms, what good would that do. The EU has already said that if we trigger A50 there is no going back and if we don't accept the terms we leave on WTO terms. Effectively neutering any say the Parliament will have on the terms because they don't have sole decision power, the EU 27 have to agree too and they won't agree with any single change our Parliament wants over and above what is negotiated.
This is far from over and May is far from out of options. The very demographics of the Leave vote must have put the fear of God, Hell and Hades into the Labour MP's who campaigned to Remain.
This is just getting interesting.