Lanna isn't
that great,
@egoo.
Let's compare her to us for a second.
Lanna:
Is a Sha'ir wandcrafter whose level rivals our Companions
- Has access to all wizard spells and thus can make basically any wand
- Has a hell of a time recharging those spells after any battle, literally takes her days, but by the same token she can fall back on wands
- Has the Spell-Reflecting crown taken from that one Westerling girl who Robb foolishly marries in canon.
Is semi-decent at intrigue given that she keeps poking around in the Imperium
Has had the Lannister wealth to back her since day one
Raided the outskirts of Valyria with Gerion
Is the Lady of Castamere
Is the head of the Golden Shields
Arranged for Marid mercenaries to side with the Lannisters
Viserys:
Is a Mythic Red Dragon Sorcerer King
- Has access to every sorcerer/wizard and cleric spell through Wild Arcana
- Has Blood Wish and Miracle
- Is a Dragon with all that entails
- Has @Goldfish gear, courtesy of Lya and our treasury
Has the Companions to cover any areas he can't (Garin for the Inquisition, Malarys for Laws, Lya for magical study, etc) and far more PCs than Lanna could ever hope to bring to the table
Has recruited dozens of powerful outsiders and three True Dragons (and one formerly True Dragon)
Is Lord of the Imperium with full control over the western coast of Essos
Is the official ally of the Shaitan and the Djinn
- This happened through us rescuing Embra, and then subsequently skinning Mammon's Aspect for a cloak and then marauding in the Plane of Fire against the Efreeti to prove our strength and commitment to the war
- And even then, they needed a powerful common enemy to consider allying with a mortal no matter how powerful
The list could go on forever, but you get the idea.
Tldr at best Lanna has bought the services of a few mercenaries (exceedingly few given that we faced, what, six when they attacked Sorcerer's Deep that first time). I genuinely doubt she had the political weight to become a full ally to any of the more important houses.
If she somehow
did get the allegiance of a house, fine. We already know from DP that the Marid are famously disunited, so it's not exactly hard for us to go straight to that house's enemies and recruit them instead.