98% Shipper Trash by Volume.

Of course I kept the high lactase persistence (LP) around the air temples, but I also showed the diffusion of that trait in the areas around the temples. This could be because of Air Nomads mixing into the non-nomadic local populations (genetically and culturally) and due to the trading/gifting of sky bison dairy products to those populations. I think the latter would reinforce the former, in this case.

Important to remember is that this map is representative of the percent of a population's LP if there is a population living in a given location. For example, for over a hundred years, there were no people living in the air temples, but if there were, they would have high rates of LP. Similarly, the Si Wong Desert is sparsely populated, but those who do populate it likely have LP (operating under the assumption that the sandbenders and other nomadic people get milk from the camelephants).

As in our reality, there are also high rates of LP in less fertile lands like deserts or higher latitudes (by the poles) and altitudes, as these regions tend to have more issues growing crops that can meet diet requirements. By having dairy producing animals eat the less nutritious crops, their bodies can basically add in the missing nutrients. This is why I have marked more mountainous regions + the Si Wong Desert as having more LP.

Version without the location labels:

Reference map (Wells 2021):

So once again I'm referencing the Stock and Wells paper, because it has really nice maps and it's pretty accessible in terms of academic language.

This map is pretty straightforward—circles represent points (areas) of origin, and the arrows denote the dispersal of the species. But for lore purposes, this requires some notes.

Flying Bison: I have marked their area of origin as being in the Southern Air Archipelago. We really don't know where they're specifically from, but seeing that there are populations of bison living in the Fire Nation (with/around the Bhanti tribe), I'm guessing they're from either the Western or Southern Air Archipelagos. And purely because the Bhanti tribe lives in the southern part of the Fire Nation, I've placed the bison as from the South. Their dispersal paths are also the most unique of the list, as, since they can fly, I imagine them flying directly to their preferred habitats, and the Air Nomads following/settling based on that.

(Really, the bison are too enlightened to be considered 'domesticated' by humans, but I included them because of their teamwork with the airbenders + their dairy potential.)

Arctic Camels: These creatures have more appearances in the Southern Water Tribe than the Northern, so I've placed their area of origin in the South. Perhaps they reached the North on trading ships or pirate ships traveling between the tribes?

Moo-sow (Cow-pig) and other pig hybrids, excluding the Picken/Pigster: The moo-sow are the only pig hybrids confirmed to be raised for their milk. Others, like the wooly-pig (cross between a sheep and a pig), are raised for specific functions like wool for clothes. But seeing as sheep in our world have been utilized for dairy, I don't think it's a big jump to think wooly-pigs would be in similar circumstances. All other pig hybrids are fully mammal (so this inference could still apply) except the picken (pig + chicken) and pigster (pig + rooster). (I don't know why they're two separate things. Weird!) Since these are birds crossed with mammals, they might not be able to produce milk. In Beasts of the Four Nations, Aang supposes that they lay eggs, and makes no mention of milk.

If the Picken and Pigster are more like chickens than pigs, they are likely to be native to A:tLA's equivalent of Southeast Asia—the Fire Nation. (Wikipedia page for the red junglefowl, from which chickens were domesticated.)

On the subject of the Fire Nation, I remembered—after completing this map, of course—that the Fire Nation has a native milk producer: the hippo cow.

Admittedly, this throws a wrench in the whole 'lactose intolerant Fire Nation' theory, but we could suppose that they are raised primarily for meat, and milk is an extra. According to the wiki, hippo cows are also domesticated in the Earth Kingdom after the Hundred Year War.

Final notes:

Non-hybrid yaks also exist and can be found around the Northern Water Tribe. Their dispersal pattern likely follows that of the buffalo yak quite closely, so they were not included in order to prevent crowding and clutter on the map.

Goat dogs and goat gorillas exist in the Earth Kingdom. While goats in the real world produce milk, these goat hybrids seem to express their non-goat 'genes' more prominently than the goat ones. Therefore, I have decided not to consider them.

New version of lactase persistence map, without labels:

Version of cattle map with labels:

And the lovely reference map (Stock and Wells 2023):