I think it can still happen, but Lily will simply become the slut Mateo meant for her to be, and in the end it can benefit us on the Corrupted path as well

The only reason I chose Mateo in the first place was because I knew he was a pervert and would turn my innocent little flower into a slut. So here's how it could possibly play out:
1. You go on the trip without Lily, Mateo will take her virginity and fully awaken her hunger for sex. She'll have her doubts from time to time, maybe even sending the Dad a text message from time to time telling him she's ok and will be back after the trip. Keeping a secret that she's with Mateo. Once she's fully corrupted and ready to come back, she'll seduce the Dad and it'll be the player's choice whether he'll be upset or going with it.
-- Upset path would be Hard NTR path, she'll turn away from the family and pursue the satisfaction of her newfound desires and run away to live with Mateo. We'll still see fractions of her life until the endgame where Mateo may be arrested for trying to do the same to another girl and Lily will be nowhere else to go. As it's the Hard NTR path, she'll be far more independent and won't care about the Dad's feelings anymore, and of course won't be sleeping with him neither but that won't stop her from making trouble for him by seducing his friends.
-- Sharing path would be Soft NTR path, where she'll keep seeing Mateo but returns living with you. She'll be trouble, a lot of naughty trouble since Mateo has unlocked her desires she must be on par with those lovely twins we haven't seen for too long (any episode without them is too long). In fact they could be fast friends all three being little sluts. Of course, you'd have to share Lily with Mateo and some other people, like Angel's father because you won't be able to stop her the young succubus by now. But in return you may get potentially: foursome with the twins, threesome with older sister, sex in risky situations, open display of promiscuity, and maybe an accomplice in the Corruption route in general.
2. The trip gets delayed, the Dad will look for Lily, hires a private investigator and eventually finds her with Mateo. Player can choose to destroy Mateo where he stands and causing trauma to poor little Lily and refer to the Upset path above, or become partners in crime with Mateo. In this case Lily will stay with Mateo for a short while, where he may or may not take Lily's virginity, but she'll still be corrupted enough to become a promiscuous little slut - but then joins the trip that happens later on. For this one refer to the Sharing path above.