Responses
I don't think it's stated but I got suspicious after seeinfg "queen sister" so I looked at the raws. Llyod calls the queen "noonim" (누님) which is something men would call a woman who is older than them (could be an older sister or a friend). If you heard "noona/nuna" in kdrama "noonim" is the more respectful version. The translation "queen sister" is quite literal but there's really no way to convey korean honorifics in english without sounding awkward.
I can't believe i just discovered that the queen is older than lloyd. But looking back it makes perfect sense