LawLu

LawLu is the slash ship between Monkey D. Luffy and Trafalgar D. Water Law from the One Piece fandom.

Canon
Despite Law's outward stoic demeanor and apathetic attitude towards Luffy, Law does seem to like him. He also seems to accept following Luffy's lead when it comes to carrying out their plans and tolerates the Straw Hat's captain taking the initiative in a lot of situations, even if it can annoy him from time to time.

The two first met at Sabaody Archipelago inside the Human Auction House, Law witnessed Luffy punch the Celestial Dragon, Charlos. He smiled at Luffy's defiance towards the World Noble and fought alongside him, as well as Eustass Kid, when the Marines surrounded the auction house. Following this, the two went their separate ways. Law and his crew traveled to Marineford during the Summit War of Marineford to assist with Luffy's escape, and then later administered medical treatment to him. As he said, while Luffy would one day be his enemy, an enemy relationship is still a relationship and that it would be a "damn shame" for Luffy to die at Marineford. He then left Luffy in the company of Jinbe and Silvers Rayleigh before Luffy could thank him.

Following the time skip, Luffy met Law again on Punk Hazard after Law became one of the Seven Warlords of the Sea, he saved Luffy and Nami from the Yeti Cool Brothers. He then asked Luffy to form an alliance with him to take down the emperor, Kaidou. Luffy agreed, making their crews allies in a relationship (which Luffy perceives to be as practically a friendship, but Law sees as more of a professional agreement). Luffy often treats him very casually, like a good friend, something which Law usually frowns upon. Law has invested enough in this alliance that, despite it having nothing to do with their agreement, he decided to help Luffy and his crew save the kids on Punk Hazard, even though he himself only viewed them as a burden. He also has a lot of faith in Luffy, as he asserted to Doflamingo that Luffy would capture Caesar without a problem. Law does seem to have some doubts about Luffy's reliability and carefree attitude. When Luffy sent Caesar flying instead of capturing him as he was supposed to, Law remarked that he knew he should not have formed an alliance with him and resorted to trying to capture Caesar himself. However, after Luffy put his faith in Usopp and Nami to incapacitate the deranged scientist, which they did, he expressed satisfaction that Luffy upheld his end of their agreement.

At the end of Punk Hazard arc, Law also objected to Luffy's decision to throw a party instead of leaving Punk Hazard, as he believed they were still vulnerable, though he still reluctantly joins them and has stew with Smoker. Though Law indicated that he wished to 'use' Luffy when forming the alliance due to the Straw Hats' great unpredictability and ambition, he instead feels like the one being used.

During the Dressrosa Arc, Law's arm severed and faced with near impossible odds against Trebol and Doflamingo, he was given a chance to have any wish granted as long as he performed his Devil Fruit's "Perennial Youth Operation" on Doflamingo. Rather than take the opportunity, he instead berates Doflamingo for underestimating Luffy (among other things), and boasts about the various miracles that the Straw Hats have performed up until now. This highlights a deep trust in Luffy, which is uncharacteristic of the strictly professional relationship that he originally intended to establish with the crew. When Law was brought to the Flower Field as Luffy fought Doflamingo, he stated that it was his fault that Luffy was brought into this matter due to the alliance. He was willing to share whatever fate Luffy suffered as a result, even death. Robin, however, corrected him by saying that Luffy would have joined voluntarily because of Doflamingo's deed. Law deeply respects Luffy for his role in Doflamingo's downfall, as shown when Law informed Bepo that it was Luffy's doing.

During the Wano Country Arc, the one thing that deeply concerns Law is Luffy's tendency to get into trouble and he even berated Luffy for complicating Kin'emon's plan due to his desire to do good. When they reunited with each other in Bakura Town, Law was exasperated and annoyed that Luffy and Zoro picked a fight against the Beasts Pirates before the plan could start. He is also extremely annoyed by Luffy's penchant to tell him what to do, since he does not want to be perceived as his henchman.

Fanon
LawLu is one of the most popular ships within One Piece fandom, with more than 3000 fanfiction on AO3. Many fans like how their relationship has evolved over time, and how Law and Luffy have developed a sense of mutual respect, and despite having opposite personalities they generally get along; while Luffy is downright silly and stupid, Law is more stoic and serious in any situation.

A comic relief in fandom is how Law very often organizes a possible plan for some mission, and Luffy does not follow it ruining it, ending up being reprimanded by Law himself. On AO3, LawLu is the second most written ship in the One piece tag, and it is the most written ship for both characters.

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Trivia

 * Luffy is unable to correctly pronounce Law's surname, so instead, he calls him "Tora-o" (トラ男), which is a part of the "Tra" in "Trafalgar" and the Japanese kanji for "male". This is often localized as "Tra-guy" in some subtitled media, or as "Traffy".