Lou is Cole's father and dancer who wanted his son to follow in his footsteps. When Cole was a child, Lou sent him to Marty Oppenheimer School of Performing Arts but Cole ran away from the school and wouldn't see his father for sometime. After reuniting with father, Cole was unable to admit that he ran away from the school and became a Ninja. Lou found out and was furious but watched Cole battled the serpentine being impressed with his son's choice. The two reconciled the relationship and have become closer as Lou once made a song to show how proud he was of him.
In "Day of the Departed," Lou wondered what was taking Cole so long to meet him, as he was looking forward to lighting lanterns with him for the holiday but Cole couldn't show because of Yang. In The Hands of Time, Cole was surprised to find his father was being held hostage by the Vermillion Warriors and with the help of Jay together they freed him and everyone else.
It is unknown what sort of relationship Cole had with his mother, as she has not yet appeared in the series.
In "The Jade Princess," he appears to have loved her as he told Wu that he was sad at her presumed passing and resorted to climbing mountains as a way of coping with her being gone.
Nya and Cole are good friends throughout the series, but in Season 3, Nya developed a crush on Cole, which caused him a rivalry between him and Jay that continued on in Season 4. It is most likely these feelings from Cole developed because of Nya giving him attention.
In Season 5, when Cole became a ghost, she supported Cole to keep on trying with his life and never give up. In Season 6, Nya ultimately chooses to be with Jay but Cole is supportive of her choice with all three remaining good friends in the end.
Seliel and Cole are good friends then love interests in the book "Who is The Phantom Ninja?" This relationship is non-canon; that means Cole never met Seliel in the events of Season 3. It is unknown whether she truly exists in the series or if she does whether Cole will ever meet her.
Cole is Wu's student along with the other Ninja. When Cole and the other trained to become Ninjas, he is shown to really care about Wu and glad to have him mentoring them. Cole is the closest with Wu, as he was his first student as a Ninja.
Like the other Ninja, Wu sees Cole as one of his best students.
Following Wu's sacrifice to defeat the Time Twins, Cole and the others were devastated by his loss and made plans to find their lost master. Cole was the most devastated by the loss of his master.
In Season 8: Sons of Garmadon, he is the main one focused on finding his master and has changed some of his habits to more driven such as giving up on sweets and training more intently.
Cole later encounters a mysterious baby while being held prisoner to the Sons of Garmadon. Cole is responsible for taking care of the baby and at the end of the episode "Dead Man's Squall," Cole is seen shielding the baby to protect it from the Bounty's crash.
In "The Quiet One," it is revealed that the Baby is Wu with Cole being surprised as he sees the infant talk and drink tea. Cole questioned this before Nya and Zane came up with a theory for it and how he'll turn back to normal very soon.
Jay and Cole are best friends throughout the series. Cole and Jay argued in earlier seasons and Cole was most likely annoyed with him, due to the differing personalities (Cole was always serious and Jay was childish and unfocused), they always have each other's backs like the other Ninja.
In Season 3, their friendship hit a rough patch when Nya developed a crush on Cole; this makes Jay upset and causes them to become rivals for her affections; which, along with Zane's "death" to defeat the Overlord serves as a main reason for the team breaking up.
In Season 4, they refuse to be on the same team again and continue fighting with each other about Nya. Jay even notes that he was more upset about losing Cole than Nya, showing the power of their friendship. When Chen forces them to duel in the tournament, the two get out some of their pent-up frustration but in the end they rekindle their friendship with Cole sacrificing himself so Jay could advance. They maintain their friendship in the next season with Jay expressing sadness (nearly crying) when Cole was turned into a ghost by Yang and attempting to move him out of his despair.
During Season 6, Cole confronted Jay about him keeping his encounters with Nadakhan a secret from him and the others, being angered by his reasons. However, Cole was overjoyed to see Jay and Nya reconcile their relationship, not even upset she chose Jay over him, showing how much they rebuild their friendship. Jay considers Cole as his best friend.
In "Day of the Departed," when the Ninja rushed to Cole's aid as he was fight Yang, Cole was reenergized and managed to overpower and defeat the ghostly master. When Cole was thought to be departed, Jay broke down crying and stated that he would give anything to have Cole back, which the latter overheard before revealing himself to be alright. Jay and other Ninja were relieved when Cole was okay and became a human again.
Like the others, Cole was put off by Zane's personality but when finding out he was Nindroid, he and the others supported and accepted their friend. In earlier seasons, Zane and Cole were best friends due to them being similar as being serious Ninja.
When Zane sacrificed himself to defeat the Overlord and was seemingly destroyed, Cole was distraught his demise and was unable to continue being a Ninja. In season 4, when Lloyd suggested replacing Zane, Cole and the others were adamant about not replacing Zane until they spotted a poster that said he was still alive causing them to enter Chen's fighting tournament to find him. After being eliminated from the tournament, Cole was the first of the Ninja to find Zane, being relieved to see him alive and well in a new form and immediately promised to break him out of his captivity. Working together, they manage to break free however, due to Cole's promise of breaking the other elemental masters out of Chen's grasps, he implored Zane to leave while he goes back. To his surprise, Zane decides to help him deeming that Ninja never leave one another behind. After a series of plans, they were successful in liberating the captives and join their allies in defeating Chen.
In "Day of the Departed," Zane and the others were very happy Cole was fine and became a human again.
They are good friends throughout the series. Kai and Cole respect each other and both are close friends. In Season 5, Kai was sad that Cole became a ghost and attempted to move him out of his sadness. Kai made sure Cole never gave up and they even took Morro down together along with Lloyd.
In "Day of the Departed," Kai and the others were very happy to see Cole return to being a human.
When they first met, Cole thought Lloyd was troublesome and would tell Master Wu to give him a severe punishment in "Never Trust a Snake." After he reformed, they bonded and became good friends to the point, that the former would prank him more often than the other Ninja.
Lloyd and Cole continue to be good friends throughout the series, with Cole giving Lloyd support which would inspire him to keep trying whenever Lloyd was feeling down in some battles against their enemies. When Lloyd was possessed by Morro, he and the other Ninja did everything they could to rescue him from the Ghost Warriors. After saving him, Lloyd says Ninjago is at risk of being in possession because of the Preeminent, but the Earth Ninja tells him they won't be able to stop her without him.
Overall, Lloyd looks up to Cole and they work together greatly. In Season 6, they worked together throughout the season. They had each other's backs and both led their friends against the Sky Pirates.
In "Day of the Departed," Lloyd and the other Ninja were glad to see that Cole was okay and became a human again.
In Season 7, Cole supported Lloyd throughout the season. One point, Cole and Kai went against Lloyd's orders so that they could take action. At the end of the season, Cole and the others let Lloyd take charge in Wu's absence.