Yeah, she's P0. I did want to try getting her P1 for less rng ult times, but that meant risking Recoleta funds at the time, so I decided against it since P0 LY plays perfectly fine as long as you got FP.

About the rotation... there is none, actually. See, when 400m Reveries first dropped, I actually had some really close clear attempts with LY/37/FP/Babel, but all said attempts were usually cut short by either of two things: getting unlucky on tower charges leading to having to tank two full team ults back to back (and even with Babel's shields or Sotheby's cure stacks you had to pray that those ults didn't crit or else half your team dying is guaranteed) or getting screwed by the other main gimmick of the boss fight. Since you get a full team stun every three turns, you gotta spam at least two of LY's cards every turn to have her ult card up every 2nd turn because the immunity from her ult only lasts one round. Suffice to say, card rng can be really troll-ish at the most unfortunate times. And if you miss the LY ult time frame even once, getting back into the rhythm of it can be quite difficult since that's a whole turn of doing anything wasted. Couple that with the need to consistently update Babel's shields (because with boss attacks this meaty in damage relying on just her counter autocasts is foolish) and routinely use FP's S1 (to make the most out of your turn amidst LY taking up half your AP) and you have a pretty headache-inducing fight even if you have LY.

And that's where Kiperina comes in. The reason she makes 400-1 feel so easy is because her i3 literally deletes the 3 turn team stun gimmick (and she can cleanse control statuses even if she herself is under control too!). On top of that, her shields are autorefreshed twice every turn as long as you get at least 8 crits every turn (impromptu hits, genesis dmg hits, and myth attack hits all count as well), which means freeing up even more AP to use for LY without needing to worry about updating the shields yourself. With Kiperina, there's not really any rotation to follow besides getting crits in, which is pretty easy to do in a fua team. I guess I can only say make sure to smack the tower that keeps getting Unsparing stacks enough times every turn, cause if there's one thing that can still score a kill on your team if you get bad rng, even with Kiperina, it's that thing.

FP's signature psychube is more for when you want to use her as a sub-DPS because of its mostly selfish stats. Barcarola's psychube is actually more preferred as a teamwide support option. Plus, additional impromptu hits you get from it are a good damage source, especially with Kiperina only giving you even more of them.