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Cole and kai grew up having a lot of playdates, with their parents being elemental masters and having to work out battle stats and stuff. They would often skip stones along the water near the blacksmiths shop, or just have little play fights and pretend to be grown ninja. Kai used to have a major crush on Cole as a kid, but never realized until adulthood, after regaining the crush in between seasons 9 and 10.
In rebooted, Cole never liked nya. He would pretend to, but was actually reflecting all the traits he loved about kai in attempts to distract himself.
Cole is gay, kai is bi for clarification)
Cole was kais bisexual awakening.
the lava duo never dated until dragons rising, with Cole finding out about kais crush through his diary entries from monstrosity. These contained all the things he liked about Cole, even admitting to collecting rocks in the realm of monsters because it reminded him of Cole. They begin to date after Cole confronts him about the letters, a few weeks pass and Cole asks for Kai to be his yang. (its accepted)
The fight they have in drs3 before Cole gets his soul sucked was mainly because Kai was extremely jealous of geo, Cole later states geo is in fact just a very close friend. Kai is still jealous either way, he just knows to control it better now.
Cole is farsighted and needs Glasses but refuses to wear them. Kai thinks this is adorable.
Cole sucks at cooking and Kai is great at it, so sometime before the merge (I have not decided a timeline yet) Kai teaches him how to cook.
Not a lava headcanon, but Kai is Korean and philipino.
Turning into a ghost left cole completely depressed and distraught. he struggled for months after returning to his human form, and even during being a ghost he hated himself and felt entirely useless to the team. Kai was also majorly affected by this and wouldn't leave coles side after dotd. He had missed being able to hug, and just hold his hand. Doomed untouchable yaoi anyone?