I think it would be prudent for. Lilly to assume he is going to say they don't live together, and be prepared for that,
It's safer to assume if the documents are to come to them, he has agreed that with them.
Prepare for the worst. Hope for the best. She's prepared for him to say he lives with her. Now she has the time to prepare for him to say he's not. As such, this is a good thing, it means she's not caught unawares.
In addition I'd prepare for him saying he wants to buy her out the house, and he takes it on, although Lilly thinks he won't go there, for him to say he needs x amount for rent, or if he lived with the woman, then x amount to stay there.
However my understanding this is about what Lilly needs to avoid undue hardship, and can he afford it. I'd also think his solicitors are preparing him. So understanding what he may try to do to limit payment, is only going to help when it comes to it.
As said, prepare for the worst, hope for the best.😔