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SPOILERS !!!!!!!!!
Spoiler
Spoiler alerttt
OK SPOILERS:
Lady Lyn does actually become sorta two-faced and you can sorta tell from the recent chapters. She realises that she loves the emperor, but its also at this time that the emperor and empress start opening up to each other and all the cute stuff happens. So Lady Lyn gets salty because she regrets getting them together and is now kinda highkey annoying from this point on.

Now that i think about it, what if Lady Lyn has lowkey fallen for the empress? Or maybe, she just wants the title of the empress, you know, power. She knows she's protected when the emperor's by her side, so the emperor falling for the empress might result on something. But, she can be also protected by the empress, right? Maybe the fragile thingy is just an act, but maybe she's really just like that. Idk..