I already explained, It wouldn't make him want to hook up with Lena any less (but after her outrage maybe he will), it will make Ivy the better girl which is what Ivy always wants.
I just don't think this would fit Ivy's established character at all -- Ivy makes it clear that she thinks having casual sex with people is absolutely fine and doesn't make someone look like a worse person. So i doubt she'd think differently when it comes to Mike. The game also goes out of its way to tell the player that Ivy already
is "better girl" than Lena -- way more charismatic, self-assured, fit, sexy, etc. She doesn't need to put Lena down, all guys already, entirely on their own, think she's the "queen bee". Remember Ian's and Perry's conversations e.g, as well as Ian's thoughts about Ivy.
I suppose this being the case of simple gossip between Ivy and Mike could be an explanation, but then it'd be weird that Mike knows about stuff like Lena blowing dudes in the club toilet, but not about fucking Axel, something Ivy also knows.