@AFWQ I stand corrected on them using the same term in both places. So yeah, I'd agree it's a bad substitution, at least in the medieval setting.
As to the usage connotations of "lass" vs "miss", though, I think you're dead wrong. First, "lass" is definitely less formal and less class-oriented than "miss", there's no two ways about it (at least as a form of address like that). If someone is "miss so-and-so" that doesn't have a lot of class implications, but referring to someone as "the miss", "the young miss" or such is definitely a sort of talking upwards--not that formal, but with distinct lower-class-talking-to-upper-class implications; so is actually addressing someone as "miss" if you know them well. "Lass" is of course a Scottish term, and like anything widespread and Scots, it comes from humble working and peasant class background. And it's used for any girl. If it has class implications it's the other way--it's a form of address you would be less likely to use to someone upper class unless you were really close to them and felt you could ignore the rules.
Finally, my (partial) Scots heritage rises up to insist absolutely that there's nothing cold about "lass"! It's a friendly, honest, easy-going form of address.