Why should Kylo be telling the truth? He’s misled Rey once already.
I don’t think he’s lying. Before he reveals who Rey’s parents are, he says she should know it and then he’s surprised that she doesn’t. Maybe Snoke manipulated his vision of Rey’s parents, as he established the connection between Rey and Kylo in the first place, but personally, I like the idea of Rey Random too much to believe that.
She does know it though. She’s the one that says they’re nobody.