Rey's lineage is going to be one of two things:

a) Kylo lied to her, and is hiding the knowledge of who she is (or he doesn't know) in order to try abd break any notions of specialness to recruit her, or,

b) Rey has zero specialness, and telling everyone in the movie that she is not special, not a Skywalker, not anyone relevant is part of the new movement for Star Wars. Luke is dead. Han is dead. Leia is (soon going to be) dead. The Skywalker lineage has ended, and it's time for a new generation.