Because I haven't compiled my notes yet, here's a bit of history for Sun Lance's origin, from near the point of timeline split (just before the first protag arrives to the Indigo Plateau...)
Sun Lance's life began to change from his peers during security meetings and discussions between the police, the Silph Corporation, and the major competitors in the space all under strict security as official Master Ball manufacturers- including the Devon Corporation. It began with President Joseph Stone taking note of Lance's detailed report about the security breach, which was only given uninterrupted because Interpol agents were changed last minute. Rather than Lance getting an invitation to join the G-Men unit, the Devon President asked that he come by as a professional to give a risk assessment on their key Pokeball manufacturing. True to his character, Lance has always been determined to help anyone who asks.
The opportunity afforded to a young Sun Lance lead to new experiences, collaborating with Devon instead about the search for his father's missing Dratini using the Pokenav app features, as well as seeing the Hoenn region with a powerful new friend. Using the technology to try to track down the dragons he had joined the police for, he became a friendly companion to even go to other regions alongside Sun Steven searching for stones. Lance and Steven's working together turned to bonding out in the field and bloomed into repressed romantic and sexual feelings. However they are both struggling with a major problem: Steven is already dating Wallace. Wallace isn't a huge fan of cave searching but suddenly he's catching feelings for Lance while engaged in his hobby outside the league... and Lance's family expects him to find & marry a woman and produce them a child in order to fulfill their final demands to become the next Dragon Master. A role he was specifically chosen to fulfill.
And so their yearning twists and turns with both of them trying to replace the shape of each other with familiar close company in Wallace and Bruno. The league rolls back around and a sense of normalcy seems to return, with the boys still texting each other throughout the league year. The miscommunications culminate in a hot, after-event party at a club to celebrate a coordinator friend of Wallace's who also happens to be a dragon tamer. Lance was invited and offered to bring Bruno out to Hoenn to enjoy the trip only for the Water specialist to directly ask him about his perceived boyfriend. Lance denied being gay, tensions rose, the vibe of the party was immediately soured, friendships were shaken. The Kanto trainers left their Hoenn friends.
Lance tried to reconcile with Bruno for the misunderstanding but his best friend felt publicly humiliated and also regretful for having invested in him. The dragon tamer hadn't even realized he was flirting at all. Meanwhile, Wallace, being the most promiscuous of them, talked to Steven directly about his feelings and offering the opportunity for an open relationship since he was clearly interested in Lance while Wallace was interested in his coordinator friend. Steven thought on the conditions and agreed but it didn't matter in the end for him as his friend had already begun to withdraw away from him.
The situation leads Lance to 'sober up' and resist the socialite lifestyle in order to focus on his objectives more. He apologized but became a lot more withdrawn and unavailable to his friends. He saw what happeneed as a sign he was too distracted from his objectives, but ultimately it was fueled by a self-loathing spiral of regret, inadequacy, and feeling trapped by his family. Time passed, egos soothed but unresolved hurt was buried.
Since Sun Lance was still working with the Pokenav, his travels finally brought him to encounter Cynthia again after years from their last encounter. With the hindsight of his lack of clarity before, Lance is more forward than ever as he's determined to try to find the wife he chooses. His asking her out for a gentlemanly dinner lead to her becoming more and more curious about this powerful champion who acts so traditional yet doesn't hold her to such standards. She tests him a bit with silly and inappropriate things but he surprisingly matched her lead in humor. No obligations dinner that he paid for turned to catching coffee and going to the museum and checking out a festival... and very intense Pokemon battles.
Despite the good times they were having together, and despite him being up front about his goals, Cynthia still rejects the offer to become his girlfriend. She admits she wasn't interested in being tied down to one person and didn't share the same life goals of raising a child, but she was happy to spend time with him. Time wasn't what he needed though- he needed an answer to his obligation. Sun Cynthia's openness about her desire to maintain her freedom and the reality of Sun Lance's family expecting him to find his life partner or get arranged a marriage finally broke his walls down. It only occurs to him now why Bruno suggested the idea about running away. He was terrified he wouldn't find something beautiful like his parents had in time- he was terrified what his family would deliver him.
Incidentally, it's about this time Steven finally became a Champion himself- which caused conflict with Wallace's ego as his rival. Despite his friend becoming more distant, Steven reaches out to Lance in his hour of need... and Lance, yet again, is always determined to help anyone who asks. Lance is not in a good position, but in a moment of feeling so alone himself, he offers Steven can come over to hang out.
Sharing the physical space with each other again after so long, and burdened with so much pain and desiring comfort, they finally hook up. In the morning, Lance realizes he "may have lead Steven on" and tries to apologize and say he still needs to marry a woman which Steven says 'fine, whatever, but can you do that later? I want to hold you.' The dragon tamer obliges.
In the days that passed from her rejection, Cynthia had thought about it a lot. He really offered her more than she ever expected- shares her interests, treats her well, apparently wasn't just trying to hook up for sex, accepted her no gracefully and doesn't harass or belittle her. Going along with Lance would get her own family off her back in a big way as they are also traditionalist and expect certain things of her, she just had written off the idea of placating it long ago. Cynthia wondered how likely Lance could change his mind about having a kid, or how open he might be to polyamory and he could find a mom that way.
A couple of weeks after she rejected him, Sun Cynthia reached out and asks if Lance wants to have another date, but also says she understands if he's done with this chapter. Steven gave him space but definitely heard the talk going on. Lance doesn't really know what to say at first- this is 'wasting time' again but he likes Cynthia. And Steven is 'wasting time' too but doesn't want to hurt him and Lance likes him too. It doesn't seem like he's getting anywhere no matter what he does. Sun Lance politely asks to check his calendar and call her back, then finally breaks down when he's off the phone. He admits how he's been rejected as a boyfriend by every girl he's wanted to see steady, but if he doesn't succeed soon, he's going to be betrothed and stuck with a mystery woman Forever.
Steven is astonished any families are still doing that in today's age and reassures Lance its okay. He tells him about the morning he left about how Wallace actually opened up their relationship at the time, so he knows what Lance has to do and he's okay with it. Lance is astonished by the idea of having more than one partner... but suddenly it makes sense. Cynthia's offer to go on more dates despite her desire for her freedom, and how Steven could come be here without cheating on his boyfriend.
Lance decides to have another date with Cynthia. He keeps cordial and a bit stiff the whole night through. Finally on their walk back, he asks what he could do to change her mind about dating him. She isn't quite sure how to answer that but she does say she'd like to see how he is in bed at minimum since she is more adventurous.
Things go well and in the morning since she still hasn't agreed to be in a committed relationship, Lance tentatively asks if she's ever heard of polyamory and she laughs at how cutely timid he is about broaching the subject. She's VERY on board and actually agrees to make Lance her official boyfriend as long as he's okay with them setting boundaries to have multiple partners.
And this is how Sun Lance's polyamorous situationship begins.