Wait for the season to end and the team to disband :P
Really though, I think that's kind of the point of it being a super team; it wouldn't be recognized as such if there were an obvious way to take them down. Typically, beating a well-known team works by exploiting a weakness. For instance, LG obviously weaker when they don't have b4nny up (not only is he their demoman, he's the holy crux of the team), so trading a scout and roamer for that pick can sometimes lead to a won fight, even though the trade is bad at face value.
Mixup just doesn't seem to have that weakness; there's no one player that stands out as being the best or worst on the team. When one person doesn't seem to be at peak performance in a round or map, another person seems to just play that much harder.
Mixup's biggest advantage is their coordinated deathmatching - sure, ruwin and enigma are crazy good, but so are the other scout combos in the game, and the same goes for every other position (Chess Club is admittedly weaker in basically every department, but they're also considered fresh talent to the invite scene). The key difference is that they're always in the right place at the right time, much like the checksix of seasons past.
To break through mixup's solid play, LG will have to force individual players out of position and work together to take them down. To me, this means playing defensively and not quite waiting for a mistake, but rather creating one; using two or three people to force a scout or roamer on the flank into a 1v2-3, and jump like crazy on that advantage. Midfights will just have to be about pushing ruwin and e` away from the fight, while still putting pressure on platinum, something I think b4nny is best equipped to do out of all demos at the top. I'd let Dave just babysit the flank rather than trying to go for uber forces, as TLR doesn't seem to know the meaning of "bad uber". Tyrone's really stepped his game up from what I've seen, but I'd still like to see b4nny being the pocket and Ty being his sexy escort, being more of a bodyguard than a point man.
Offclassing and kritzing might be a way to score some rounds, but I honestly think LG will have try more than just the standard stuff. I don't know why I even wrote all that because I'm probably not saying anything new/interesting/useful/correct, but whatever, figured I'd make a last post before I went to bed. No matter who wins, I wouldn't expect a complete stomp - we all know LG's tendency to step up to the plate at LAN.