The party has to wait until another incursion happens, and it will, before they can enter the deeper lairs.
That is a good question. How I would interpret it is they are not lost in the inner lairs. When the party claims an anchor and the lair collapses, the party within it returns to the Kingdom of Dreams unless they move to another lair before then. Otherwise it would be much harder to play a higher level game. There is no version of Plane Shift in The Nameless Grimoire.