Okay, to put this to rest... Euphie thought Gino was cute and wanted to sleep with him. That's more or less the sum total of their 'relationship' so far. Lelouch was busy and Euphie was stuck on the island all year after previously spending years at college with other college students, doing things that college students do.
What I'm saying is that she probably wasn't a virgin even before Gino, because Britannia has more equal gender norms at the highest levels of society.
No one got pregnant, undeniable proof of the relationship didn't end up on the front page of a newspaper, so Lelouch doesn't see a problem with Euphie having some fun with Gino. Because it would be hypocritical of him to throw stones when he's maintaining a relationship with Kallen and Jeanne in addition to Euphie.
Lelouch didn't know about Gino and Euphie until this action was taken. He noticed because, in tying to schedule the 'dates' he went on with Euphie, seeing Gino come and go from her quarters wasn't all that difficult. The fact that Gino was being discreet enough that someone had to look for the affair to find it is a good thing. Because it means he's not being sloppy or lazy.
...on the note of Gino and Lelouch becoming romantically or sexually involved, it could happen.