She also commented in the same comment that the Empire was "Co-led" by a Jedi. So yes, Vader is a Jedi. I think I vaguely recall a comment that Palpatine wasn't a proper Sith either but since I don't have it at hand I won't comment. To be honest with Kylo at least you could argue pretty easily that he isn't a 'true' Sith but rather a fallen Jedi- he doesn't use the title Darth and given his partial training imo it's entirely possible he doesn't even know what the Sith are beyond "like Vader"."The first Order is lead by a Jedi", is he talking about Kylo? Cause Kylo ain't no Jedi, he fell to the dark side and became a Sith. I'm not even that into Star Wars but how is someone who is writing a big damn Star Wars fanfiction not understanding the very simple Jedi/Sith dichotomy the series is famous for? Would you call Darth Vader a Jedi too!?
The problem is that Lily's a bit of a contrarian edgelord, as well as a leftie of the "Punch Nazi" variety. So she likes the idea of sexually liberated Sith women being objectively superior to canon-designated good-guy Jedi. Unfortunately, the Sith are always exclusively shown as fascist-coded antagonists in Galactic Civil War/Disney Star Wars. So her ideal character can't exist as is in canon because Aliana has to be both a Sith (for the contrarian points), and anti-fascist (meaning she needs to be fighting the designated Sith aligned faction on ideological grounds).
To handle this dissonance she makes sure to stress that Aliana comes from a long line of "Sith" who-whilst apparently still adhering to the core Sith Code, also have split off from canon depictions of the Sith back in the SWTOR era. This means she can effectively invent her own interpretation of the Sith Code which favours the elements she admires (personal independence and embracing emotion as a source of strength) whilst sanitising the elements she doesn't want to deal with (might-makes right, treating people around you as either tools to be manipulated or rivals to be subdued). However, this still leaves Sith in canon who aren't following her divergent code and whom she doesn't wish to see absolved of their sins (Vader and Kylo). Arguing that rather than Sith these people are dark Jedi (and as such that their actions are a fault of Jedi teachings) allows her to position Aliana as both a model Sith and innocent of any facist tendencies (because the Empire/FO are now led by rogue Jedi and not Sith.
Even better, by redefining the iconic Star Wars Sith as Jedi pretenders, Lily gains an in-universe excuse to paint Aliana as unfairly marginalised. Both Luke and Leia are shown as prejudiced against Aliana for being a Sith, both reasoning that as such she and her family are automatically bad people. While one might argue that Aliana herself is a bad person and that Sith as a whole in Star Wars canon are all evil by default, from the perspecitive of the version of Star Wars constructed in TSR this is false.
In Lily's personal version of Star Wars Aliana is a fundamentally moral person who does no real wrong and her mother was the same. Therefore Luke was effectively comitting a hate-crime when he murdered Aliana's mother because True Sith in this universe aren't evil. Likewise when Leia is electrocuted by Aliana, Leia is in the wrong. In Lily's canon the Sith are merely misunderstood and every comment Leia makes to the contrary is just racism that Aliana eventually responds to in a fashion Lily feels is justified.
To handle this dissonance she makes sure to stress that Aliana comes from a long line of "Sith" who-whilst apparently still adhering to the core Sith Code, also have split off from canon depictions of the Sith back in the SWTOR era. This means she can effectively invent her own interpretation of the Sith Code which favours the elements she admires (personal independence and embracing emotion as a source of strength) whilst sanitising the elements she doesn't want to deal with (might-makes right, treating people around you as either tools to be manipulated or rivals to be subdued). However, this still leaves Sith in canon who aren't following her divergent code and whom she doesn't wish to see absolved of their sins (Vader and Kylo). Arguing that rather than Sith these people are dark Jedi (and as such that their actions are a fault of Jedi teachings) allows her to position Aliana as both a model Sith and innocent of any facist tendencies (because the Empire/FO are now led by rogue Jedi and not Sith.
Even better, by redefining the iconic Star Wars Sith as Jedi pretenders, Lily gains an in-universe excuse to paint Aliana as unfairly marginalised. Both Luke and Leia are shown as prejudiced against Aliana for being a Sith, both reasoning that as such she and her family are automatically bad people. While one might argue that Aliana herself is a bad person and that Sith as a whole in Star Wars canon are all evil by default, from the perspecitive of the version of Star Wars constructed in TSR this is false.
In Lily's personal version of Star Wars Aliana is a fundamentally moral person who does no real wrong and her mother was the same. Therefore Luke was effectively comitting a hate-crime when he murdered Aliana's mother because True Sith in this universe aren't evil. Likewise when Leia is electrocuted by Aliana, Leia is in the wrong. In Lily's canon the Sith are merely misunderstood and every comment Leia makes to the contrary is just racism that Aliana eventually responds to in a fashion Lily feels is justified.