I'm going to preface this with the fact that I love Lyse, and I enjoy having her in the story and on screen.
That said, let's be honest about the fact that their handling of her was ham-fisted at best.
Right off the bat, her story doesn't track so well with what's shown. First there's the reveal that she's been living a lie, but that's over because Papalymo's gone now. This does one positive thing, and recontextualizes a few old combat scenes and shows us in spite of her inexperience, Lyse was at least always one hell of a fighter.
It comes at a cost to Stormblood in the present though, in that she'd been working with the Resistance of Ala Mhigo as Yda with Papalymo. Why do they recognize her as Lyse at all? The boots and Conrad's elephantine memory, I guess. It still doesn't come off well. On top of that, much like Minfilia, all of her work with the Resistance happened off screen, so we don't feel or see the weight of it.
So she's got two bad vibes right off the bat, losing some lead way to build momentum as likeable in the story. It's not helped by her temper during the Ala Gannha segment where she asserts that it's her home too, in spite of not being there for twenty years (it'd be like me going back to the state I was born in, and claiming it's my home, in spite of living in a completely different place with different customs my whole life).
So her first impression is really really bad, and a lot of people cannot relate to how she grows. Lyse grows without a mentor figure throughout the story, often relying on her own memories and strength of will to see things through with an occasional nudge here or there from other characters (Sometimes just be observing and listening to them).
Personally, I think she's a brilliant character falling victim to incredibly bad execution/conveyance. Not many people can get over her terrible intro, or the bad conveyance of her growth. Bear in mind one of her most poignant and philosophical lines comes in the same quest where she and you are tasked with picking up poop. It's when the Mol children ask her what a nation is.
LYSE: "I heard the Mol move from place to place-- that the gods tell you where to go. That must be hard on you all..."
BOISTEROUS MOL BOY: "Hard? I do not understand. Why is it hard? It is better for the animals to move-- to have more food to eat and land to roam. To stay in one place is harder, no?"
RESERVED MOL BOY: *nods* "...From the heavens comes the rain which nourishes the soil. From the soil comes the grass which nourishes the beast. From the beast comes the flesh which nourishes the Xaela. Ours is the soil of one and all."
BRIGHT-EYED MOL GIRL: "But you Westerners are like the Domans-- you live in the same place. In villages. And all of the villages in one place are part of a, "nation," yes?" *gesturing wildly in the air with her hands* "Hien speaks talks about nations sometimes. When he was injured, he spoke of Doma in his sleep, but I did not understand his words."
WILLOWY MOL GIRL: "Whenever I ask him about Doma, he just smiles and looks to the south... It reminds me of my mother when she waits for my father to return from a long journey... But Hien will not wait any longer, will he? Because you came for him. To take him back... because his nation is more important..."
LYSE: "Um... I'm not sure how to answer this... A nation is a place, I suppose. A place... and the people in it... and maybe the things, too. But more than that, it's the history, the traditions, the words. The stories we tell ourselves and our children. Everything that came before and everything that comes after. The place where we were born is part of who we are. We carry it with us, no matter where we go. Whoever... whatever we become, that part remains-- that links to our fathers and their fathers before them... It's not important to everyone, I suppose, and that's fine. But it's important to Hien. And to me..."
Not many people can relate to Lyse, simply because of who she is. She is a self described patriot. Not very many people can or will admit to that in this day and age. It also doesn't help that it's brought up in a pick up poop quest, and then she is immediately sidelined for the rest of the Doman arc while Hien stands center stage (Though through Bardam's Mettle we learn that Lyse is slightly more adept at combat than Hien, finishing second at Yol "taming" after the WoL).
Brilliant character, crappy conveyance. Literally.