This is going to sound silly to some, but consider this. I'm a big fan of the Transformers Beast Wars series, and one character in particular embodies the Lawful Evil persona to a T, or so I belive... Dinobot.
Dinobot is a former Predacon (bad guy) that turns on Megatron (his leader) because he feels that the strongest and most intelligent should rule, and he felt that his leader led his men astray from their intended goal for no good reason. As such, the Preds gave Dinobot the boot... and Dinobot then decided to vie for leadership of the Maximals (good guys) to take his revenge. Optimus Primal (the Maximal's leader) accepted the duel and showed him compassion when Dinobot was hanging off a cliff... Primal demostrated that there was strength in honor, something that Dinobot held dear. (Maybe Dinobot's more Lawful Neutral... meh).
As a character, he's the largest of the group, and with the exception of Prime and Rhinox (his alt form is a Rhinoceros... go figure), is easily the strongest on the team physically. He has a rivlary with the team's "Rogue", but it's kind of a friendly back-and-forth (but not at first) in their differences on how they should deal with situations; one one level, they think alike -- do what's most effective to succeed, but where the Rogue prefers stealth and backstabbing, Dinobot prefers the "honorable" charge ahead and take all comers. He is normally all business, ie everything in his life revolves around battle, and feels that a well-planned strategy combined with brute force can solve any problem. Aloof, abrupt and to-the-point, he often mocks the Maximal's "twisted" sense of Good every time the team gets screwed by it.
By the same token, I can see your Monk as the standoffish "tough guy" that would prefer to take the shortest and most effective route to success, but goes along with the Good guys because he finds a greater strength in teamwork. He's the Shadow of Sonic the Hedgehog, the Reggie of the Archies, the snarky foil to the party's do-gooder leader...
If you have access to any Palladium RPG books, look up the recommendation on how to play the "Aberrant" alignment; it describes Lawful Evil morality to a tee.