Going back to OP's post. I think the writers had decided to go in that direction by the time they started working on ARR (never having played Legacy, I can't tell you anything about the characters in storyline then). I actually think revealing Yda to be Lyse works in a couple different ways (although I will admit I personally dislike Lyse as a character). If you look at it a certain way, a lot of Lyse's motivations come back to Yda.
Until the end of Stormblood Lyse has basically defined her life by Yda and her memory. Yda was a hero in the rebellion against the Mad King (I would assume she was AT LEAST 15 years old then since it's implied she played a significant part and wasn't just a child tagalong, so that would make her at least 10 years older than Lyse) and when Ala Mhigo fell to Garlamald and their father died, Yda managed to escape with Lyse to Sharlayan, and eventually became an Archon. She eventually also became part of the Ala Mhigan Resistance (Lyse tells you that she was caught trying to help people escape and was executed). When Lyse stepped into the role of Yda, it was a mixture of not knowing what she wanted to do with her life and wanting to keep her sister's name and legacy alive, as well as keeping morale up since Yda was considered a hero by the Ala Mhigans.
Even after Lysa put aside the role in a lot of ways she's still defined by Yda, and a lot of her character development is actually shifting away from that and finder herself. Lyse was five when she escaped Ala Mhigo and probably shouldn't have all that big of an attachment, but it was important to Yda. She scorns and berates the Domans when they don't want to rebel against their Garlean oppressors, Yda never stopped fighting the Garleans. She despises people who collaborate with the Garlean regime, Yda rebelled and the Garleans eventually killed her. In the last act of Stormblood, the red Ala Mhigan outfit Lyse wears was Yda's. Lyse says Yda wore it as often as as she could and Lyse wants Yda to be a part of Ala Mhigo's liberation. But by the end of Stormblood Lyse's decisions and actions seem to be based on what she's learned and experienced throughout Stormblood. She's not just acting out of Yda's memory anymore. it's subtle (and honestly poorly done) but it's there.