So for my campaign I have 4 players, and one of the players (my buddy) has had every single one of his characters hated by the party (even after we had a TPK); even though out of game everyone jokes about it and even he is a good sport about it, but I want to find a way for his character to at least be tolerated in game so the others have a reason to bring him with them on adventures. Currently he is playing a Great Old One warlock who is obsessed with gaining arcane power, no matter what he has to do (sort of like an addict); the other player characters are an Air Genasi monk who is seeking to strengthen himself for vengeance and values loyalty above all else, an Aasimar divine soul sorceress who is fairly altruistic but will do whatever it takes to protect her sister (other PC), and a Tiefling dragon soul sorceress who is not so bright who has to continuously hide her identity and has an obsession with bears.

tldr; How can I get a Lawful Evil untrustworthy PC to be trusted by Neutral Good and Lawful Good PCs

Simple. Don’t allow evil characters in a hero campaign setting. This is what I do. That or play an all evil campaign. 

Honestly the pcs have no reason to trust him. I assume they know he is evil, or at least not a moral person by action he has done in game. So why would they trust him, he is evil, and they are good. They should smite him. That's what I would do if a devil, which are lawful evil alignment, came up to my sorcerer who got his magic from some divine holy bloodline.

All that aside what you need, if you are willing to let him play a evil character, is a reason they need each other. A good example is the Dragon lance books. The party didn't trust Raistlin but they needed his knowledge, and he needed the group's protection. 

So maybe have the group find a map to some arcane treasure but only a being with a pact to the old ones can read it. The group needs him to read the map, and he needs them to protect him along the way. Once they find it who knows. Be prepared for him to betray the group, or the group to kill him if he goes all evil. If it's trust you want have him change his alignment, cause it's not wise to trust evil characters.

unless someone changes their alignment/s, this isn't going to fundamentally change. it's much like the MCU Thor and Loki relationship.

"I trust you, you betray me, and over and over we go."

Any relationship where the essential goals and ethics aren't aligned will just end up in some betrayal somewhere down the track.

But as we see, Loki ends up taking Thor's advice about character growth, before meeting his end in Infinity War.

In regards to him being evil we are only a few sessions out of the TPK, so no one knows he is evil and his last character was Lawful Good and everyone still disliked him. The characters he tends to play are eccentric by nature (his second character was a stripper, and his LG character thought he was better then everyone else) so I'm trying to find a long term reason to keep them working together, even if not trusting each other

Thanks for the idea about the map that helps a lot to start off their relationship

Quote from VengData >>

In regards to him being evil we are only a few sessions out of the TPK, so no one knows he is evil and his last character was Lawful Good and everyone still disliked him. The characters he tends to play are eccentric by nature (his second character was a stripper, and his LG character thought he was better then everyone else) so I'm trying to find a long term reason to keep them working together, even if not trusting each other

 So in other words, he's been using his characters vicariously to be a jerk.  Evil characters and jerk characters are going to be untrusted by the rest of a good-party.  The best you can hope for is some form of obligation that prevents the rest of the party from killing them off.

As a player, he needs to learn how to be a courteous player.  It is okay to have an eccentric character.  It is okay to have an evil character.  It is okay to have a stripper character.  But that does not mean their character has to be intolerably obnoxious.  And playing a character like that while claiming "that's just how my character is" is a crock.  They created the character, they determine it's behavior, they consciously decided to make their character obnoxious, and the reason why is because they want to do whatever they want and not be saddled with any consequences.

You fix this by applying consequences.

Pull him aside out of game and tell him that he can keep playing his characters the way he is, and that's fine.  But from now on, his actions are going to have consequences.

Character's a stripper to does lewd things all the time?  No NPC takes the character seriously and/or treats them like a trash/2nd class citizen. Or one day a group of drunks decide they really like the character and when told "no", get violent about it.

Lawful good character makes sure everyone around him knows how great he is?  More powerful NPCs so up to challenge his claims.  Or his boasting alienates key NPCs and they refuse to interact with him or the party while he's with them.

Evil character willing to do anything but ANYTHING for power? Eventually, the authorities are going to know about most of the things he's going to want to do for the sake of power.  When he does bad things, chances are, as a player, he's not thinking about real world consequences, and so doesn't clean up after himself.  If he DOES clean up after himself, have him make a skill check to sanitize his crime scene.  Have law enforcement on the look out for him; if the party fails to defeat the wandering law enforcement guards/officers/whatever, he gets slapped in magic-dampening manacles and arrested.  If he slays the law enforcement party, the standing order for all other officers becomes "kill on sight".

There's a little misunderstanding here. The player is a nice guy who isn't making characters for the sake of being a jerk, out of game everyone enjoys the characters he makes and their antics, about consequences there already has been some in the third session after introducing the stripper character he drunkenly ran around the town we were in screaming out songs in the early morning so he got arrested and got the whole party barred from the town, his LG character was an a-hole because he felt he had some great destiny ahead of him and because of it one of the other PC's got him sent to an insane asylum and let a local mob boss Assassinate him, his new character hasn't done anything wrong as of yet except trying to charm the monk to tell the group the truth when the monk and aasimar were having a dispute and the monk broke his nose for that; I've also talked to him out of game and he's been trying to make his new character more likeable and though the other characters have had a little reason to stay together his character has been trying to work with the others and everyone shrugs him off. As the DM I'm trying to just find reasons to get the others to find a use for him.

Ah.  That changes everything then.  A little charisma and a sense of timing transforms what would be a usually obnoxious character into everyone's favorite life of the party.

This is much easier to work with, especially since as a lawful evil his behavior will be manageable.

In-game, the character can try to make a logical appeal to the rest of the party, so long as he hasn't done anything up to this point to blatantly harm or betray any member.  Ends justifies the means is a fairly standard argument that nearly any alignment can use depending on the interpretation of their alignment.  The fact that he probably could have, but has not yet harmed any other them, and has proven to be a reliable source of "making the people who want to hurt us go away faster" (assuming he's ever hit any enemy ever in combat) could also be leveraged.

The way I have personally made my own evil characters function in good-aligned parties was make it clear that the characters have the same goal, and then reinforce that good-characters can't afford to kill the evil character because of some specific ability it has or niche it fills that makes them absolutely critical to the success of the party.  Here are a few personal examples.

In a 3.5 case, my chaotic good barbarian (who was convinced beyond the shadow of a doubt that he was actually a paladin) was the party's defender.  The rest were wizards and sorcerers.  If the barbarian died, the squishy spellcasters would soon follow.

In one 4e case, it was the fact that my gloom pact hexblade at level 1 could 1-shot the party's defender, which meant being able to one-shot any other party member of his choice... and yet he refrained, and instead acted as the heavy-hitter for the party.  The fact that he was charismatic, and despite being evil was that brand of evil you get in Gru (Despicable Me) and Heinz Doofenschmirtz (Phineas and Ferb) helped greatly.

In a recent 5e game, I played a cleric healer who was born with a psychological disorder: namely, she was a clinically diagnosed sociopath (lawful good due to early intervention of the church which pretty much hammered a moral code into her from a logical basis in the form of rules-made-into-habit).  She was also the party's only healer, and its only utility character, all the others having overspecialized in hitting things, not getting hit by things, or getting hit by things and just giggling at its attacker.  Her illness made her exceedingly pragmatic (manifesting in a dampening of of her emotions), and somehow she ended up as the de facto party leader.

There's no reason an evil character couldn't be in a party. I had a concept for a CE priest of Talos - drunk and mad as a badger but convinced that the party 'do the will of the stormlord' and so he's there to make sure they do. Obviously they might not, he's totally crazy (wears an eyepatch but has both eyes, talks to the clouds etc). He's chaotic evil but not disruptive to the point of 'kill the pesants for lolz' - more likely to terrorise them via a sermon about being hit by lightning than actually shoot lightning at them