Well food is heavily based on the environment of the surrounding area, not just animals but the resources to cook those animals (like the kind of wood/burning fuel or even stuff to make containers for cooking).
The freljord probably has no shortage of wildlife and fish to consume, so meat is probably common. Grains and vegetables (or heaven forbid, fruit) are probably a lot rarer and more often fought over (especially grain for a multitude of reasons). I don’t know if the freljord has fertile areas, but I’m assuming they have a harvest season unless it’s always winter. If it’s always winter, then they probably get grains through trading furs across ships (because Demacia won’t trade with them) which means they can have a wide assortment of grains for their meals.
Noxus probably has a lot of different dishes due to having lots of different territories. They probably mix a few dishes together, but this is more noticeable in the outer territories or in the war front where cultures mix. Noxus prime probably doesn’t mix dishes unless a high ranking military members request it at a dinner. The lack of good farmland however might make import dishes more common.
Demacia has loads of farm and hunting land which probably makes their diet the most realistic in a fantasy setting.
Piltover and Zaun probably have a lot of fish, but being big port cities have access to more grains, fruits, veggies, meats, and spices than any other faction and probably makes those dishes more common because of how small the city is. But being the techo city it is, they’ve probably advanced methods of cooking so higher ups or wealthy people have automatic stoves or something (someone with better knowledge of how cooking appliances developed could be better at explaining this).
Bilgewater is literally enjoying all the pleasures ship trades have to offer, but probably have a large amount of fruit in their diet cause scurvy. Actually I doubt they use bread much because mills need a steady supply of it but idk.
Ionia: look it’s basically how asiain cuisine developed.
Shurima: basically how desert dwellers found food.
Icatha: the Void ate it.
Bandle City: Tristana was cooking fish so Yordles eat. They probably have more modern ways of cooking given how Heimerdinger works with technology.
Who did I miss?!