I've had an idea of attempting to run a simple module such as lost mines, but having a few people attempting to fit an awful stereotype. For example, we could have a extreme rules lawyer, a dice fudger, murderhobo, etc. And I cant do anything about it, and just go along with the game as well as possible. 

I'm sure that this would be an absolute disaster, but that's the point. How do you think that this would go? And if you played, what would you play?

It depends on the party, really.

Still, you're saying "a few", that means at least half the party. I'd say just go all in, have every player have a stereotype. It's not fun when youre aying it straight while half the group is messing you about. I'd also consider just doing a oneshot - it mightnget old pretty quick.

Stil, if the table has the right sense of humour, then it could be a laugh.

As Linklite said, as a one-off it might be tolerable, but the novelty will probably be lost within the first hour. Negative stereotypes like these are usually tolerated *until* they are obvious. Once they're out in the open, it's just annoying. Everyone will be racing to destroy the game their own way because there is no point in being subtle.

Instead you might consider giving the players "Player Feats" that let them "cheat" with rules. Maybe an ability that resets every short rest, and/or scales with proficiency.

Oh, it would just be a one shot. Anything more would be bad

Just player stereotype or character, as well? like a horny bard and an edgy warlock and a rogue who steals from the party and a lawful stupid paladin. 
Either way, it could be really fun, as long as everyone buys in. 

I think "farce" has it's place in an occasional one shot, I wouldn't limit it to just player stereotypes, but play on both halves of the screen.  Like you need to prematurely reveal the BBEG that they "should" have known all along (though it would have actually been impossible from players vantage) and then you go on to recite like a five page metaplot of everything that built up to the moment, stuff which the players were utterly unaware of.

Also devastating random encounters and too fragile bosses.

Also have them come up with back stories, but keep messing up creating "shining moments" for characters based on some other characters' backstory, like character B saves character A's long lost true love (and is now true to character A).  Character C finds character D's birthright and proves worthy, stuff like that.

I've toyed with doing a sort of "anti game" like this and call it the Lost Mind of the Philanderer, so the DM doesn't even get the title right.

I think, for people with the right sense if humor, it could be really funny and for a session. You just want to sure that your not rude to people who may be somewhat of one of the stereotypes, just less extreme.

I have the perfect character for this. He's a Chaotic Evil Conquest Paladin who is a living loaf of bread, and he's definitely a murderhobo. He could also be the one that metagames all the time. For example, part of his backstory is, he once burnt down the tavern of another bread loaf paladin, who then decided to become an adventurer as well to teach players to respect NPCs. It'd be fun for them to meet up at some point.