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Lyrica's personality is based on her tendency to scheme.  She's the one who keeps the sister organized in fights, and plans things out. Her kind of leading the band behind the scenes is a headcanon I actually found in one of LyricaLive's Raiko x Lyrica fanfics, which I integrated into the story. Lunasa meanwhile I view more as a "serious loner" type, who really only opens up to her sisters. My favorite illustration of the sister's personalities is from Aya Azuma in Alternate Facts in Eastern Utopia: Merlin is super into her performance, Lunasa is silently enjoying the concert, and then you have Lyrica: eyes wide open eagerly watching everything play out.

File:AFiEU Prismrivers Article 2.jpg

As for where I got their personalities: Perfect Memento in Strict Sense has comprehensive descriptions of the Touhou 6-9 cast.