Got this from Wikipedia.
I think it’s interesting to look at this graph in terms of migration and colonization. Northwestern Europe is VERY lactose-tolerant, and most white Americans are descended from NWE stock, so there’s plenty of lactose-tolerance here (with African-descended and Native Americans the exception). Likewise with the lactose-tolerant whites in Australia (from NWE), and the lactose-intolerant Aboriginal Australians.
Then you have that belt of southern France, Italy, and the Greek peninsula where lactose tolerance drops; continuing that trend westward, it would make sense that Spain and Portugal would have low tolerance as well. Portugal and Spain had a strong influence in the European infiltration of South America, and as the indigenous South Americans have little lactose-tolerance (much like their North American counterparts) you still have an overall low incidence of it in South America today.
And in Asia, where lactose-tolerance is VERY low, you have a gray zone (no data) in Mongolia, but considering that the Mongolian diet is rich in yak milk, yak butter, and so on, I suspect their lactose-tolerance is fairly high. Then you have India, where there is a spike in lactose-tolerance, perhaps because of the reliance on milk, which is the basis of the Hindu reverence for cows?
I’m curious about the sharp divide between the southern African countries and the central ones. Ancient tribal lineage? Herding culture vs. non-herding? Effects of the US-colonial-era slave trade and mixing with westerners?