This excerpt uncovers one of the trickier aspect of depicting a lie: we have to be able to see it clearly. While I admit much of that may be in context we don’t have here, it’s not clear from the reactions of our narrator who is lying and when.
This is why it’s always wise to drop a clear hint for your reader. It can be as simple as “I didn’t believe that for a minute” from your first person narrator. Or a physical tic from your lying character. Or a declaration of nerves from your POV character if they’re the one lying.
Of course, you don’t want to be blunt, cliche, or obvious, but at the same time make sure your reader can have that “I knew it!” moment when they see the lie.
Author - Speaker - Coach