I think Parliament is morally obliged to now honour the result of the vote (if the matter goes there) & move forward.
You mention the P word - Parliament. This is what the case was about - getting Parliament to have a say about what sort of Brexit we are aiming for. So far most MPs have said that they will honour the result of the Referendum - which was only really a statement of "we'd like to leave the EU". No clarification as to how we should do it or what we should put in its place was sought.
If they won't then Theresa May will need to look into repealing the Fixed Term Parliament Act.
And just how does Theresa May do this, without being a dictator? She has to lose either a vote of Confidence or a majority of the House have to vote to Repeal the legislation.
How does she get us some MPs who will listen to the Nation? Does she go round telling x, y and z that they have to resign, because they don't agree with her and she says so? Then does she personally select the desired candidate? Then does she say to the voters in x, y, z's constituencies that there won't be an election because she has selected a, b, and c. This could happen if they were the only candidates standing, and they were returned unopposed. So does she ban the other political parties, because they dare to think differently?
Truly we would be well on the way to fascism if that happens.