Ty Lee's relationships

Family
In the episode "The Beach", we learn that Ty Lee had 6 other sisters, and she said that all of them looked exactly like her. She didn't want to be part of a "matched set" anymore, so she joined the circus to be different.

Mai

 * "Come on, let's get out of here!" - Ty Lee to Mai after striking Azula in The Boiling Rock, Part 2



Even though they have different personalities, Mai is Ty Lee's best friend. Unlike Ty Lee, Mai is a lot colder and calmer. Ty Lee seemed to have met Mai when she was at Royal Fire Academy for Girls. She knew her enough to play a trick on her and Zuko with Azula and not worry about it damaging their friendship. Ty Lee occasionally teases Mai for her crush on Zuko, a romance she in fact encourages. Mai seems to be better friends with Ty Lee than Azula, because when Azula is not around, Mai doesn't follow her orders. When they exchanged stories during the episode "The Beach" and when Ty Lee told hers, Mai pointed out that she needed ten boyfriends because of she didn't get enough attention when she was a child. During "The Boiling Rock, Part 1" she and Mai went to the Boiling Rock, even though Mai went to talk to Zuko and Ty Lee followed Azula. After Mai had betrayed Azula and saved Zuko, Ty Lee blocked Azula's chi in order to save Mai. The two girls were locked away in the prison, or another one (as the Boiling Rock was only for the most dangerous of prisoners and the girls met the other Kyoshi Warriors who were not imprisoned there), where Azula would never have to see them again.

Ty Lee and Mai presumably remained friends after their release from prison, especially given that Ty Lee selflessly gave up her freedom in order to save Mai's life.

Zuko

 * "I know you." - Ty Lee to Zuko in "The Beach".



Ty Lee shows to have known Zuko since he was little since she was comfortable enough to play a prank on him. When she joined up with Azula and Mai, they followed Zuko and Iroh across the map, trying to find them. She seemed to accept him without problem on his return from exile. During The Beach she went on vacation with Zuko, as she was accompanying her friends Mai and Azula. When tensions rise, Zuko calls her a "circus freak" and berates her for her boundless optimism. She then starts to cry and tells them why she is a "circus freak". She then pressured him, along with everybody else, to find out why he was so angry. Like her friends, Ty Lee sympathized with Zuko's inner turmoil and confusion. After she and Azula fled to another gondola after fighting Zuko and his allies in "The Boiling Rock, Part 2", she looked uneasy, possibly worried about Zuko.

It can be presumed that Ty Lee and Zuko are on friendlier terms with each other now that the War is over.

Sokka

 * "Is it just me or was that guy kind of cute?" Ty Lee to Mai about Sokka in "The Chase"



Ty Lee and Sokka first met in Omashu during a prisoner exchange, and naturally were enemies of each other. When Ty Lee and her friends pursed the Avatar and his group through the woods in "The Chase", she chose to fight Sokka. He was easily disabled but managed to hurt her hand when he used his skull as a shield. He and Katara were almost finished off when Appa disposed of Mai and Ty Lee, launching them into a nearby river. Ty Lee later told Mai that Sokka was "kinda cute".

Ty Lee met Sokka again when they fought in "The Drill", giving him a flirtatious look and him responding with a smile and a friendly "hey". However, Katara knocked him back into his senses.

Ty Lee called Sokka a "cutie" and approached him when he and Toph tried to stop Azula from conquering Ba Sing Se. Slightly uncomfortable, he remarked that he was "kinda involved with Suki", who Ty Lee had previously but unknowingly encountered in an earlier engagement. She then smiles goofily at Sokka and attempts to block his chi. Sokka awkwardly dodged her punches across the floor, with Ty Lee stating "It's like we're dancing together". She disabled him when Azula ended the fight.

Ty Lee and Sokka met again when Sokka and Zuko were rescuing prisoners at the Boiling Rock, but Ty Lee was so busy fighting Suki that she had no time to acknowledge her attraction to Sokka.

Ty Lee and Sokka met after Ty Lee was released from prison following the end of the War. At Zuko's coronation, she appeared before him, dressed as a Kyoshi Warrior. Sokka accused her of trying to attack again, but Suki revealed that Ty Lee had joined her team, as they finally made up during their time in prison. By this point, she had also reconciled with Suki, who is Sokka's current girlfriend.

Ty Lee and Sokka are presumably friends now that the War is over, but since he is in a relationship with fellow teammate Suki, it is likely that Ty Lee respects this fact and has moved on.

Katara

 * "Ty Lee. She doesn't look dangerous, but she knows the human body and its weak points. It's like she takes you down from the inside." - Katara to the gang in "The Drill".



Ty Lee and Katara have never properly interacted onscreen, but they first fought each other during a botched prisoner exchange in "Return to Omashu". When Katara attempted to disable Mai using Waterbending, Ty Lee used Chi blocking to disable Katara, rendering her totally defenseless. This nearly resulted in Katara getting taken down by Mai. Although Katara escaped unharmed along with her friends, Katara developed a deep fear of Ty Lee, as she normally can't fight without Waterbending.

Katara and Ty Lee fought on several occasions afterwards, including when Azula and her friends chased down the group in "The Chase" and during "The Drill". However, in this later engagement, Katara successfully fought off Ty Lee by shoving her into the Fire Nation Drill by bending the liquefied slurry, and hatefully called her a "circus freak". Ty Lee got Katara captured when she disabled her in "The Guru" while they were in Ba Sing Se.

Katara and Ty Lee never fought again after that engagement. After Ty Lee betrayed Azula and was imprisoned, she had a change of heart and befriended the Kyoshi Warriors in prison, as shown when Ty Lee announced that to the group after the War ended. It is safe to presume that the girls are now on friendlier terms with each other.

Kyoshi Warriors

 * "We’re going to be best friends forever!" - Ty Lee in Sozin's Comet, Part 4: Avatar Aang.



Naturally, Ty Lee and the Kyoshi Warriors were enemies during the War. They first encountered each other when she and her friends tracked Appa down in a forest, where the Warriors had just nursed Appa back to health after weeks of hardship. Along with her friends, Ty Lee defeated the Warriors with her Chi blocking. She taunted them by saying, "You're not prettier than we are!". After the battle, she and her friends stole some of their uniforms to infiltrate and capture Ba Sing Se for the Fire Lord.

Ty Lee later fought the Warriors' leader, Suki, when she was escaping the Boiling Rock Prison along with Sokka and Zuko. This time, Ty Lee failed to overpower her, as Suki had managed to block all of her Chi blocking moves.

After betraying Azula along with Mai after the battle, Ty Lee was imprisoned and somehow ended up with the imprisoned Kyoshi Warriors. While together, the girls bonded with each other and apparently Ty Lee was forgiven for their previously-unpleasant encounter. After she taught them some Chi blocking, they invited her to join their group, which she gladly accepted.

After the War ended, Ty Lee and her new team were released from prison, and she made up with her former enemy Suki. She stated at Zuko's coronation as Fire Lord that now they can be best friends forever.

Azula

 * "Well, Azula called a little louder." - Ty Lee in Return to Omashu



Azula and Ty Lee have a somewhat complicated relationship. In many respects they're opposites. Azula is mean-spirited, a great strategist, intimidating and socially inept. Ty Lee is none of those things. Ty Lee met Azula in the Royal Fire Academy for Girls along with Mai. When Ty Lee completed a trick that Azula couldn't, Azula pushed her down and laughed, however, right after that, she joined in on a prank on Mai and Zuko. When Azula came to recruit her for a mission to capture Zuko and Iroh (and soon after, Aang) Ty Lee at first declined because she was happy with her life at the Fire Nation Circus. Azula then tricked her into coming along after making her show incredibly dangerous. While Ty Lee at one point regarded Azula as a friend, it is apparent that she fears Azula and is hesitant to disobey her. She seems to have more respect for Azula then Mai does. When Azula told them to follow the Avatar's friends in "The Drill", she continued the pursuit, even jumping into the slurry which Mai refused to go near. Ty Lee seems to care about Azula's opinions of her and other matters. When Azula insulted her during "The Beach", she immediately began crying. Azula apologized, showing she does care to at least some degree about Ty Lee's feelings. When Zuko called Ty Lee a "circus freak", Azula laughed. During "The Boiling Rock, Part 1", she goes to the Boiling Rock prison with Azula. She fights alongside with her until Azula finds out that Mai is helping Zuko escape. Once Mai is captured and Azula prepares to strike her down out of rage, Ty Lee chooses to block Azula's chi to save Mai. Azula had them locked away.

Like Mai, Ty Lee seems to have little respect and sympathy for Azula, as she did not even mention Azula after the War ended. She has instead moved on and made friends with the Kyoshi Warriors, whom she promptly joined. It is unknown if she feels sorry for Azula's traumatic defeat. However, given her sweet disposition, she is more likely to express sympathy than Mai.