Hi docker
The key thing here is that she has to do a legally binding agreement with her partner on the ownership of the house. If they split up, they will be in an even bigger dispute.
Although the mortgage might be in his sole name, they can agree that she pays half the mortgage and "owns" half the house.
It seems odd that the lender will give a mortgage to Mr X, but not give a mortgage to Mr X and Ms. Y. However, that is the type of oddness which happen from time to time. If your sister has a bad credit history, it would probably bar them both from borrowing.