So, short prediction, referring to bodies for the sake of convenience:
Kogahara won't immediately believe the two, or will be otherwise interrupted/distracted. To clarify "Lemon" will accompany Kogahara to that Crepes-Party and Kogahara will ruminate during that party on what she'd been told, but have her doubts. They'll stay up till midnight with that binge-watching thing. "Lemon" will fall asleep or doze off shy of midnight (as previously established, the swap happens when both are asleep at midnight and they both fall asleep just before). Lemon will wake up, again in her own body. Since Lemon doesn't know what "Lemon" told her in the first half of that evening, she'll play along as best as she can, but this will deepen (or outright confirm) Kogahara's suspicions regarding Lemons and WhatshisfaceSunao's body swap.
There might be a couple chapters where Kogahara is on the fence regarding the body swap idea, while the MCs don't know whether she believes them or not.