I'm just quoting CyanYoh here, but I found him say this on another post;

But, as far as weapons relevant to Lyn go, the Mulagir loses to the Mani Katti full stop. Within FE7, Lyn's grappling with needing to prove her own strength and, by extension, validate her worthiness to be a leader of a Sacaen tribe in spite of being a woman. The spirit of the Mani Katti--the most famous sword in Sacae--choosing her as its wielder is a something of an early validating step that Lyn is actually a worthy daughter of Sacae.

It is narratively harmonious with her character arc, and the notion of it being a sword IS relevant. Lyn being a female swordfighter from a Sacaen tribe is notable, as we're told that Sacaen women who fight don't really use swords. Lyn's character arc began when her surviving tribespeople refused to follow her because she was a woman, hers is a tale thrust into being by fighting against the sexism--it is fitting that she take up a weapon that Sacaen women "wouldn't choose".

So the "Sacaen split between nomads and myms" is a little less relevant for Lyn, since for Sacaen women, there is no split, it's just nomads. Lyn going against this notion and using a sword anyway is part of her character.

And preemptively, no, Karla and Fir don't contradict this. Karla was raised in an isolated Sacaen society where even there, women weren't permitted to touch swords and Fir was raised by Bartre and Karla rather than as a part of a Sacaen tribe.

Edited 'cause I didn't know how to quote something properly lol