Worldbuilding: Marriage and Partnership
It's lore brain time again! This is my biggest swing in the dark yet so feel free to correct me/raise points!
Demacia - The most conservative and familiar in terms of marriage, though we'd have to see if anyone specifically decided it should be a man and a woman. If someone or something did, then I'd imagine same-sex relationships are either "don't ask don't tell" or allowed to exist but not marry. Otherwise, see Piltover.
Noxus - Marriage feels like it would be less common than just about anywhere else with the practice - but that isn't to say it's uncommon. It seems impractical for some of the population, given that a large percentage of it is is away at war and only one partner, or none, can stay home to manage a household. That said, nobles definitely do marry to carry on bloodlines and alliances (probably only heterosexual marriages allowed) and tradespeople and craftspeople with stationary jobs may also marry (less restricted). There is one system of partnership that I can see being used in Noxus: the ancient Greeks encouraged homosexuality among soldiers so that they would fight more fiercely for their boyfriends. In Noxus, love for the sake of war might be encouraged in couples of any orientation. (Darius and Quilletta?)
Freljord - We know that their system of partnership involves oathsworn (which can be applied to close friends as well as less close partners) and bloodsworn (who are sometimes sexually involved, though the term is also applied to sisters). This system is rooted in polyandry thanks to the Freljord's matriarchal society - one woman has several "husbands" so to speak. But that doesn't mean one man couldn't be bloodsworn to several women; he just doesn't have a harem in that case like he would IRL.
Piltover - I assume Pilties have a take on marriage similar to the real world. You can choose to have a fancy celebration (which is what would usually happen if you're a noble or upper-class), or not. Heterosexual and homosexual marriages would be allowed, but nobles would typically prefer straight marriages because bloodlines and whatnot.
Zaun - I don't think there is enough information for me to guess on this one, though there seem to be married couples (Ekko's parents?) so it could be inherited from Piltover.
Ionia - Not enough info. All we know about is heartlights from a human point of view, which can be heterosexual or homosexual. Vastaya - at least Lhotlan - do seem to marry in a fairly conventional sense, but no word on whether same-sex partnership would be allowed. (Neeko's existence points to "yes"; we know vastayan reproduction is magical and it could possibly take place between a same-sex couple.)
Bilgewater - Probably no formal institution of marriage, though there may be civil unions that are celebrated with copious amounts of alcohol.
Shurima - Varies from tribe to tribe. Some may do things "normally," some could be polygynous or polyandrous.
Targon - Not enough info, but I imagine the ancient Greek battle-partner system could exist here too (Pantheon and Atreus?).