Thank you so much for the ask!
I really had to think hard about who I was going to talk about, since I have so many characters to choose from. Then I decided that I should pick someone whose backstory might not be fully described in the actual story, and I thought of someone!
Sairina, the main villain from my Eothiriel Swan Lake AU fic The Horse-Lord and the Swan Maiden (which I will actually start writing... at some point... not sure when... but eventually)!
***TW for mentions of death, murder, kidnapping, and miscarriage***
Sairina's name is Quenya and translates as "magic." Though it is technically the adjective form of the word (magic carpet, magic beanstalk, magic ring, etc.), it sounds like a stereotypical fantasy villainess name and it suits her (the grammar police can suck it).
I should point out before I go any further that one way the "canon" of THL&TSM will differ from Garo/Garthad Estel and the book canon is in the severely underdeveloped/ignored/forgotten/neglected character Gilmith, the sister of Galador (First Prince of Dol Amroth) and the daughter of Imrazôr and Mithrellas. Sairina is a descendant of Gilmith, and in this AU, Gilmith's descendants are all women and they are "witches" (will be explained more a bit later). There will be a descendant in Garthad Estel (faceclaim is Asli Tandogan), but she and her ancestors will not possess any magic, and Gilmith will not be as disrespected, hence the reason why her daughters hate the House of Dol Amroth in the Swan Lake AU.
According to Tolkien Gateway, Gilmith's exact birth year is unknown (this is my shocked face). However, she is referenced as being born either in 2004 TA (the same year as Galador, thus making her his twin sister) or c. 2000 TA (making her older and the first child of Imrazôr and Mithrellas). Either way, she does not receive as much recognition as her brother because she is a woman (as is common with Tolkien), and in this AU, Gilmith inherits all of her mother's Elven magic, whereas Galador only has prolonged life from both parents, is tall, and has more stamina and physical strength than typical Númenóreans. Shortly after her children were born, Mithrellas snuck away during the night and left her family behind. Gilmith and Galador were raised by their father, and given that Mithrellas fled, it is safe to assume that she was not fully willing (which is a theory within the fandom), and that Imrazôr was kind of a piece of crap. Imrazôr gave Gilmith the Faramir treatment because she was more powerful than her brother, and Galador, despite gaining a princedom and everything that belonged to his father, was also jealous of his sister and turned a blind eye to their father's cruelty towards her.
Over time, Gilmith grew to resent her father and brother (rightfully so), and was also angry for being deprived of an inheritance, despite being the oldest child (if she was born in 2000 TA) or her brother's twin (if she was born in 2004 TA). And one day, just like her mother, she disappeared and was never seen or heard from again. Well, not exactly... she actually settled on the island of Tolfalas/Tol Falas and turned it into a sort of Amazonian society made of Peredhil rather than warriors (although some of them were probably warriors). She would travel along the coast of Belfalas and south toward Umbar, basically having one-night-stands with men there and then giving birth to their daughters on her island. Her children continued this practice, and the women were forbidden from marrying (because in Gilmith's view marriage is overrated and her parents weren't exactly the glowing example of a happy marriage). And because having children out of wedlock is a big no-no in Gondor, she's essentially giving them the middle finger.
Gilmith placed an enchantment on the island, making it appear to sailors that the island was uninhabited, and anyone who tried to step foot onto the island with ill intentions would be pulled out to sea by the tides. Eventually, some genius thought that it would be a good idea to send young girls to the island who were accused of witchcraft (or the Middle-earth equivalent of a witch hunt). Parents also cast their children who were born with disabilities into the sea because Gondorians hate imperfection, and so some of the inhabitants of the island were the outcasts of society (hence why I said "witches" earlier). Gilmith's children would care for boys who were abandoned by their parents because they were disabled/sickly and would use their magic to heal them or make them strong enough to be sent to live in Umbar (because no boys allowed on the island). In my headcanon the Haradrim are more loving towards children with disabilities than the Gondorians. As a sort of partnership with Umbar, many of Gilmith's descendants allied with the Corsairs in attacking Dol Amroth, either creating storms that put Dol Amroth at a disadvantage or joining the Corsairs in land attacks. After all, "the enemy of my enemy is my friend."
But I'm kind of rambling now. Let's get back to Sairina.
Sairina was born in 2966 TA. In 2986 TA, at the age of 20, Sairina traveled to the mainland and met a man named Imrahil, who was then 31. She fell in love (as one does) almost instantly. She did not know his true identity, and though he seemed to return her feelings, her love for him blinded her to the truth of who he was. Sairina's love for Imrahil was so great that she not only broke her people's law that prohibited her from visiting a man more than once, but she was willing to violate the law against marriage and leave her sisters and her home forever to be with him. One day, she spoke to him of her feelings and asked if he would make her his wife. I think everyone can safely assume that things didn't go well.
Imrahil admitted that he was already engaged (to the woman who would be his wife and the mother of his children), but as it was a political marriage, he felt nothing for his bride-to-be. He also said that the best he could do for her was make her his mistress because he needs sons. Two questions entered Sairina's mind: Why did Imrahil need only sons? And how did he know that she could not give him any?
And so, she questioned him, and he told her who he was: the future Prince of Dol Amroth. He also said that he learned about her identity and her ability to only give birth to daughters from his sister, Ivriniel. At that moment, Sairina realized that Mithrellas' power was not only passed down through the daughters of Gilmith's line but also through Galador's. Fun fact (okay not so fun fact), the only women in the line of Dol Amroth are Ivriniel, Finduilas, and Lothíriel. I don't know exactly what power Finduilas would have had, but it was not compatible with Sauron's, and it was considerably weaker, and so as Sauron's power grew, Finduilas slowly diminished, until she passed away the following year. Ivriniel (at least this version of her; she'll be way different in Garo/Garthad Estel) is shrewd, no-nonsense, straightforward, so I think the gift of clairvoyance would be fitting for her. Either just from listening to what Imrahil said of her or having seen them together, Ivriniel was able to figure out who Sairina was and where she came from.
Well, needless to say, Ivriniel doesn't last long and soon dies in a "tragic accident." Imrahil marries his bride, and their first son, Elphir, is born the following year.
Heartbroken, Sairina returns to Tolfalas and is brought before the matriarch (aka the oldest living descendant of Gilmith at the time) and is banished from the island for breaking three of their laws, the first being the law about marriage, the second being the law about visiting a man more than once, and the third being harming/killing another woman for any reason except if she poses an imminent threat to the one who harmed/killed her, to herself, or to others (I'm kind of making up these laws as I go so just bear with me). If Sairina had violated only one of the laws, she would have received a lesser sentence (house arrest for a month). If she had violated two of the laws, she would have been imprisoned in a very unpleasant cell that provided little shelter from the elements. But because she violated three, she was banished. Sairina could argue that Ivriniel did pose a threat in that she could reveal to others who she was, but that was not seen by the elders as reason enough to kill her.
After she leaves the island for the last time, Sairina wanders the mainland between Umbar and Belfalas. She sleeps with men and becomes pregnant a few times, but because she no longer has the support of her sisters and is in poor health, she loses all of them, which only adds to her grief and anger. She listens to the gossip of the region and learns that Imrahil and his wife have had two more sons over the years and that the Princess of Dol Amroth is with child again, and she wonders if Imrahil lied to her about having no fondness for his wife (of course, it could have started out that way and they could have grown to love each other but Sairina's not exactly in a good headspace). So, she puts a curse on the Princess: that she will give birth to a daughter and that bringing her into the world will claim her life. In 2999 TA, Lothíriel is born and her mother dies (but don't worry, Ivriniel and Imrahil's wife are alive and well in Garo/Garthad Estel).
Twenty years later, the War of the Ring ends, with Sauron and his Ring destroyed, the Haradrim and their allies defeated, and Prince Imrahil of Dol Amroth and his Swan Knights and soldiers lauded for their valor. His daughter, Lothíriel, turns 20 and comes of age, and she is regarded as being the fairest maiden in Gondor, second only to the new Queen of the Reunited Kingdom. Sairina wants to see for herself if the rumors are true, and not only does she learn that the princess is indeed as beautiful as the rumors say, but also that she possesses great power -- far greater than the gifts her aunts possessed, and greater even than some of Gilmith's living descendants. Sairina wants it for herself, and so she seeks the help of an old acquaintance of hers in Umbar. She plots to kidnap the princess, and using her ability to change/alter her appearance, she can easily trick the princess into leaving with her. However, she will need a distraction, so she enlists the help of the Corsairs, who are more than happy to seek revenge against their old enemies.
And I won't say anymore because that's where the fic will actually start.
As far as the Swan Lake aspect, Sairina is the role of both Von Rothbart and Odile (using her shapeshifting powers). My faceclaim for Sairina is Eva Green. She has been in several medieval/historical roles, but mostly I imagine Sairina as Milady de Winter (The Three Musketeers: D'artagnan) when she's wearing her hood, Sybilla (Kingdom of Heaven) during her visits to Umbar, and Morgana Pendragon (Camelot) the rest of the time. Which is funny because my faceclaim for Lothíriel is Katie McGrath in her role as Morgana Pendragon. It's the battle of the Morganas!!!!
So, anyway that's it. It ended up being way longer than I expected, which is a good thing! You don't realize how much you've developed an idea until you write it out. So, thank you again for asking this! It really helps me get my ideas organized and more developed, especially because I'm so forgetful!