https://en.wikipedia.org/wiki/List_of_Bandai_Namco_video_game_franchises
Namco Bandai owns the trademark to Dark Souls. While FromSoftware is the IP owner, if Solaire were to get into Smash it would require the effort of Namco Bandai. I don't see them going for Solaire over Lloyd, nor do I see them getting two DLC slots.
The Justia website is specifically the retrieval of legal trademark information in America. An American trademark doesn't mean much to a Japanese company who develops and publishes their own game in their home country of Japan, all it means is that Bandai Namco is in charge of managing the IP in America. This situation is most likely the way it is to make localization and marketing easier for FromSoftware, who probably doesn't have much interest in internally localizing and marketing the game for Western audiences.
I have an uncle who's a lawyer and he compares the situation to a YouTuber working with a network. The YouTuber forfeits all of his content to a network, who receives the money in exchange for what is essentially royalties, typically leaving a cut of 20-30% to the network in exchange for all the responsibilities they don't want to have to deal with. Just like a YouTuber can let their contract run out and drop their network in exchange for a new one, FromSoftware could easily do the same to Bandai Namco if they wanted to. They obviously don't and consider Bandai Namco a good publisher for their work, which is why you see the American copyright constantly being renewed.
As I said before, this is a situation that wouldn't affect both a Bandai Namco-published overseas, FromSoftware-owned and published in Japan IP in Solaire and a bona fide, 100% Bandai Namco owned IP in Lloyd both getting in, as it wouldn't be Bandai Namco getting two reps. ESPECIALLY since this is a game being developed fully in Japan, and all Bandai Namco would need to do is okay the character for release in the game outside of Japan, something they would absolutely do considering FromSoftware can drop them as their overseas publisher/IP handler any time they want.
Also, in no way does Lloyd have more of a chance than Solaire. Just because Joker made it in doesn't mean every 2.5D anime-esque JRPG protagonist has a high chance. Joker is likely going to be a one-of-a-kind addition, with other wildcards similar to Master Chief, Lara Croft, Dante, 2B, Geralt of Rivia, Dovahkiin, Pip Boy, etc taking the other spots. Solaire fits into that bunch a lot better than Lloyd does, especially considering he's not even close to being the most popular, recognized, or even beloved Tales character; Yuri Lowell and Millia Maxwell have Lloyd beaten by a million miles in that regard. And even looking outside of popularity and recognition/lovability, in what way would Lloyd even come close to being a great pick for a Tales Smash rep? Velvet Crowe has all 3 of Yuri, Millia, AND Lloyd beaten in how well she'd fit into Smash; she has a demon-possessed arm and a general Smash-feeling design, tons of in-game moves that fit Smash really well, and a revenge-fueled backstory that could be used exceptionally well for vocal taunts. And a Scarlet Night themed Final Smash? A match made in heaven!
Three Tales reps that completely obliterate Lloyd, and I don't think any of them have any chance of making it in over Solaire. Why are you so convinced Lloyd will make it in?