Not a "Who's Lukka-san's parent?" Just accepting the fact that because they say Hi it's alright? Feels like a supernatural series.
i've been calling lukka "alien," "creature," "some sort of bug," and "little beast," but given the shape of the scarf's bow looking a bit like butterfly wings, i think she's meant to be taken as some sort of fairy or similar entity.
i especially think this might be the case given that so far lukka has been referenced multiple times during discussions of weather phenomena, such as in chapter 1 when hoshi was asking about auroras and someone replying they haven't seen lukka around, and the guy here in ch 3 joking about lukka's sneeze causing wind gusts. however, nothing has been stated explicitly in the text as to who or what lukka actually is yet; all we know is that she's a little girl.
as an aside, did you notice that among her drawings, lukka included some reindeer and a fox, which are animals exclusive to the north pole? kind of an interesting detail for a girl that lives at the south pole.