It’s not lying. Fat and overweight mean different things in this context. Fat is a pejorative word, carrying a negative connotation. Overweight is a statement of fact
The gf isn’t saying, “I’m fat,” as an acknowledgement of her weight being over the recommended bmi, she’s actually saying, “I’ve gained weight, and I feel ugly and I’m concerned you won’t be attracted to me anymore.”
How to respond to gf saying "I'm fat"
She gained some weight but she is not fat at all!
How Meta’s New Face Camera Heralds a New Age of Surveillance (dnyuz.com)