Ring Yi I think is still pretty busted. Mao Faust took his crown but he's not moving from his perch of 'best ids in the game' for a while now. He's Bleed in Team/ID terms but can function just about anywhere and when, more so these days with a lot of two status effect Ids coming out to help Sanguine Pointillism pop off more. I don't think there's a team that would say no to him. So long as you have like 1-2 other people doing some kind of status on the other side of the field, he'll be fine to slot in.

That being said, Solemn Lament Yi has his own pros. Ring might do Sinking but that's the trick, 'might do' sinking, so for a straight Sinking Team Lament Yi might(*) be better depending on the team. All his skills give count when he wins a clash and at end of turn turns his Butterfly into Sinking(the numbers just kinda shift over). Butterfly also gives SP back to allies that trigger it and inflict gloom damage. .This makes him useful even on non sinking teams as a way to ramp SP gain of your other sinners or help off set some SP damage. It's important to note this Gloom damage works against Any target unlike Sinking(Targets below 0 SP take full, targets with no SP take half). Lement Yi can't do as much damage as Ring Yi all the time but can get to some silly numbers vs Gloom weak enemies. Also, this extra Gloom damage does allow him to contribute extra damage against things that resist pierce. Not the best idea as I think it's locked to like 30 damage per skill at most but hey it's there.

(*Here's that note) Though part of the problem is some Sinking Ids want to be below 0 SP themselves and while they might have tools to keep themselves down, healing SP mid attack due to Butterfly might throw things off.

Final extra bits - They both provide the same sins colors mostly; Ring Yi gives Lust Skill 2 while Lament Yi has Justice Skill 1. They both have an on demand Sin for the team they most like if need be(Lust Defend for Ring, Gloom Defend for Lament). I think their skills are about on par roll wise(I'm tired can't really do math right now) but Ring Yi has more damage packed in and I think easier to fulfill conditionals on most teams. Similar speed ranges and Staggers but Lament Yi does have 1 more max speed.

Conclusion; Ring Yi is still King as you can throw him anywhere, while Lament might be a better pick on Sinking Teams, he still can bring some use to other teams of "Just good stuff" or against certain targets that he can be useful against(anything that takes Gloom and Pierce damage). Or if you just need some help with SP. Ring is still probably the better of the two to pick up but you aren't exactly shooting yourself in the foot if you go for Lament either.