(This has also been sitting in my ask box for way too long but yesterday’s ep gave me the dosage of Lisia I needed to motivate me)
May and Max remain fairly close as adults! They both still live in Hoenn, though in different cities. May lives in Sootopolis, but travels a lot for her work as a Frontier Brain, spending a lot of time at the Battle Frontier while Lisia remains closer to home as the Sootopolis Gym Leader. Max took over the Petalburg Gym from Norman and was the Leader there for a while, but later moves to Mauville with Tory, giving the Petalburg Gym to one of his top assistants and becoming Tory’s right hand at the Mauville Gym. He and Tory are also (part-time) Researchers! They mainly use the high-tech available to them in Mauville (and thanks to Tory’s expertise) to collaborate with Brendan and the other scientists in Mossdeep.
As for the various relationships, they also all get along pretty well!
Lisia – Max: Lisia easily comes to consider Max as her little brother as well, but Max finds her (and her fanbase) a bit overwhelming, especially back when they first met during his and May’s initial journey through Hoenn with Ash and Brock. While he prefers to spend time with her in smaller doses, Max respects Lisia as a trainer and Gym Leader, and enjoys discussing that with her as it’s their main common point (apart from May). Lisia on the other hand would rather take her baby brother shopping or out to a cute cafe then talk about work! She has definitely invited him over for training only to turn it into a trip into town instead. Max will complain, but he does enjoy spending time with her! They’re a lot closer than he lets on.
Lisia – Tory: Similarly to Max, Lisia easily thinks of Tory as a younger sibling and the two actually get along a lot more “obviously” than she and Max do. When he first started his journey, Tory tried out quite a few different paths, including coordinating. Lisia was someone he admired for her confidence and ability to bring a smile to others, so they had a lot to bond over from the start! He does enjoy going out to cafes with her and they regularly meet up, both to catch up as friends and as Gym Leaders.
May – Tory: They’re very close! Having known him, essentially, for as long as Max has, May was very pleased when she found out he and her brother were a couple (which is why Max tried to keep her from finding out for as long as possible). When Tory first started trying out contests, he was hesitant to reach out to May for advice, but the moment she found out he was interested in them she took him under her wing. It was actually thanks to May becoming his mentor that Tory reunited with Max and grew close with him. They remain very good friends and Tory still views May as a mentor, often visiting the Battle Stage to train with her. In turn, May also considers Tory an inspiration as he’s grown and come into his own as a trainer, adopting his own unique style she can learn from.
The Cousins: Levi’s quite a bit older than Trixie and Nils, so he’s not as close with them growing up. Later on, however, Nils ends up coming to him for advice quite a bit once he begins exploring different paths for his future. Nils becomes interested in fashion, eventually becoming a PokeStylist. While Ione is also in coordinating/performing world, being the same age as Nils she doesn’t have quite the same experience as her older brother. Nils goes on to design quite a few outfits for Ione (and Henry) once they’re teenagers and rising stars in the performing/coordinating/fashion world.
Trixie and Evan realllly don’t get along that well, both being very stubborn, aggressive, and direct/blunt. While she’s only a couple years younger, Evan sees Trixie as just a little kid who’s just trying to ride his coattails, while Trixie sees Evan as a pompous, rude [expletive] who thinks he’s hot stuff just since he got lucky and did well as a rookie. They’re not each other’s primary rivals, but they definitely are rivals.
Trixie has a mixed relationship with Ione. On the one hand, she doesn’t like how Ione used to tease her baby brother, but on the other hand she’s also (totally not that much!!!) afraid of Ione’s affinity for ghosts and ghost-types. They’re one of her weak spots, so while Ione doesn’t go out of her way to bother Trixie or anything, nonetheless Trixie is wary of her. The fact that Nils is nonplussed by the ghosts and teasing and even grows to love designing spooky themed outfits for Ione, Henry and their pokemon… she doesn’t get it. He’s stronger than her.