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 Meta’s New Face Camera Heralds a New Age of Surveillance (dnyuz.com)
How to respond to gf saying "I'm fat"
She gained some weight but she is not fat at all!