Informant is grandmother, currently living in Florida having lived most of her life in New Jersey. I have never heard this saying before nor has anybody I’ve asked.
This saying always comes after somebody has just forgotten what they were going to say— lost train of thought. Reenacted by her and her granddaughter, this is how it goes:
Granddaughter: “Hey Bubbe, guess what?”
Granddaughter: “Actually, I forget.”
Bubbe: “Well then it must have been a lie!”
You’re supposed to say that anytime somebody forgets their train of thought. It’s a pretty cute thought and people in the room laughed when they heard it. I think it also highlights one of my grandmother’s core values which is honesty. The joke is funny because it discounts whatever one was trying to say, but forgot.
“Doesn’t matter, it must have been a lie! You’d remember it if it were true” Bubbe tells me.