In this case you are correct. "I spot a lie" and "I spy a lie" both mean the same thing. It's very common for children to play a game called "I spy." In the game, one person says "I spy something red," (for example), and the other children have to guess what it is. You are correct. Both statements mean "to detect" or "to notice" the lie.

"I spy a lie" means the same as "I spot a lie" and "I detect a lie", but is usually said slightly humorously, because of the rhyme of "spy" and "lie".

Carolyn Coogler has got it in one. All of these mean that you 'see' or 'detect' a lie.