So far, Live Twins have been an engine in control heavy decks like Eldlich. This is because they cannot properly set up a board in a pure build, since without Live☆Twin Home, a single hand trap negates the play. That is, until Live☆Twin Trouble-Sun arrives in Dawn of Majesty!
Trouble-Sun and Extension
The rays of extension shine brightly with Trouble-Sun's searching ability. Going first, Live☆Twin Lil-la and Live☆Twin Ki-sikil are likely to eat a hand trap like Effect Veiler or Infinite Impermanence. But with Trouble-Sun, you can search Live☆Twin Lil-la Treat or Live☆Twin Ki-Sikil Frost!
While it was possible to draw an extender like Backup Secretary, that requires many copies of combo extending monsters. That means a trap-heavy build could run into consistency issues regarding drawing enough Traps to be relevant.
Trouble-Sun and Consistency
Consistency regarding drawing into a Live Twin wasn't particularly a problem. Between Secret Password and Live☆Twin Home, you're very likely to get to a Twin on turn one. However, another Twin searcher means getting to use Secret Password for something else.
Secret Password can search for Evil☆Twin Challenge or Evil☆Twin GG EZ, two cards that solve possible problems for Trap-heavy builds. The opponent can go into their Battle Phase to force out an Evil☆Twin Lil-la pop, but with Challenge, whatever happens to your dastardly duo is irrelevant.
On the other hand, GG EZ can protect backrow from the likes of Lightning Storm and Harpies' Feather Duster. These roles are usually left to the unsearchable Solemn Judgment, but now it can be saved for more precise negation!
Since Twin searching is now the job of Trouble-Sun, Secret Password is better used for searching these traps. You could feasibly drop both traps to one copy and still see them often. The power of Trouble-Sun is of role consolidation.
Trouble-Sun, Life and Death
While Trouble-Sun's heal-and-burn effect may seem negligible, its power shines in a Trap-heavy deck. Outside of the aforementioned Lightning Storm, Spell and Trap removal are most effectively used against actual Trap cards. This means Trouble-Sun is likely to stay on board for a long time.
Many OTKs in Yugioh focus on dealing 8000-9000 damage, meaning Trouble-Sun can potentially mean another turn! Live Twins have especially good top decks, with one Live Twin potentially creating a pop or a draw, alongside an Unchained Abomination.
That is not to discount the burn, either. Evil Twins do not deal that much damage, and even with Accesscode Talker and two direct Evil Twin attacks, it is not enough for a KO. Combined with Trouble-Sun's burn, it could potentially eek out enough for a game. It could also be cheeky combined with clever combinations of Lil-La's burn.
Conclusion
Trouble-Sun benefits all versions of Live Twin decks and hybrids. In combo variants, it likely beats out Home as the extender of choice. But especially in Trap variants, Trouble-Sun does everything a control deck could ask for. Viability skyrockets in the shine of this powerful new searcher from Dawn of Majesty.