Is the damage really that bad? Sometimes it looks a lot worse when we realise we're the ones that did the damage. If it is a bad as you say then tell everybody you either damaged it by doing what you really did or if you have to lie then say you got real horny one night, hired a hooker to come over, hang out with you for a little bit, things got out of hand and that's that some damages happened.
Find a deal on the same or similar lino and replace it. Its easy to scrape it off the K3 board or subfloor then find the new product and an installer.