Lucina shouldn't be there then. Also there's other protagonists in Radiant Dawn that cause game overs when they die such as Sothe and Elincia. I know you haven't played the Tellius game though. It's weird as they don't have any traditional lords. They're pretty different from the other games of the series, plot in particular.
I've been trying to break it down, here's what I've got
Have the "Lord" class, always cause a Game Over when killed: Marth, Sigurd, Seliph, Leif, Roy, Lyn, Eliwood, Hector, Chrom
Lords in all but name, always cause a Game Over when killed: Alm, Celica, Ike, Micaiah, Corrin
Not Lords strictly speaking, but always cause a Game Over when killed: Sothe(?), Kris, Robin
Have the "Lord Class", but don't cause a Game Over: Elincia, Lucina
Honorable Mentions
Gets a "Rapier" weapon, but isn't a Lord: Caeda
Is Blood Related to a Lord character, but isn't one anyway: Lilina, Lissa, Emmeryn, Owain
Share a unique ability with the "Lord" character: Azura, Xander, Ryoma, Camilla, Hinoka, Leo, Takumi, Elise, Sakura
This took way longer than it should have to break down, almost like it's an arbitrary distinction or something.