There are a few things to consider.

1. The “Middle East” is a large area where lactose tolerance varies widely. Many lactose tolerance maps tend to aggregate by country, which can be deceptive, because countries may have subgroups separated by tribe or ethnicity which show large differences in lactose tolerance. It’s more useful to look at “hotspot” maps that ignore borders and simply show clines of lactase persistence.

2. Cattle domestication does not confer lactose tolerance. All dairy animals were initially domesticated for meat, not milk. Dairy production came much later, after selective breeding for milk production. And by “much later” I mean thousands of years later. Instead of saying “cattle were domesticated 10,000 years ago”, you should ask “when did dairying become significant?”

3. Consider which dairy products were historically in use. Milk spoils quickly, especially in warmer climates, so the primary dairy product in many cultures was never milk, it was some milk derivative, like cheese or fermented products. These can have much lower lactose levels than milk.

4. Lactose tolerance is not a binary, it’s a spectrum. A person’s level of lactose tolerance depends on how much lactase enzyme he produces per day in adulthood. The difference between people is in the amount of lactose can they eat or drink before getting unpleasant symptoms.

Many of these variables are not obvious on lactose tolerance maps because they don't show what criteria was used to define "lactose tolerance." How much lactose, in what form, and at what rate should be tolerated before you call a person "lactose tolerant"?

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All of this still ignores the most important evolutionary mechanism, which is selection. Lactose tolerance doesn't just depend on the presence of dairy cattle, it also depends on how important were dairy products to ensuring survival and reproduction? So long as a person has dairy alternatives to provide sufficient nutrition, there is no evolutionary pressure to develop lactose tolerance. It’s only when dairy products become critical to survival or reproduction that a selective pressure develops.

You can see an example of this in one of the major lactose tolerance hotspots in the world, which is northern and central Europe. Dairying is very old in this region, but lactose tolerance is only about 3,000 years old. Before that, people owned herds of dairy cattle but lactose tolerance was low.

This tells us that somewhere around that time, something changed that suddenly made lactose tolerance critical to survival. Perhaps climate change, perhaps war, epidemic, whatever. Something that reduced agricultural land or agricultural productivity, and forced people towards pastoralism. This change need not have lasted long, maybe only a few generations. But during this brief period, Europe went through a strong selective sweep in favor of lactose tolerance.

See, for example, these papers:

• Bersaglieri, T., Sabeti, P. C., Patterson, N., Vanderploeg, T., Schaffner, S. F., Drake, J. a, … Hirschhorn, J. N. (2004). Genetic signatures of strong recent positive selection at the lactase gene. American Journal of Human Genetics, 74(6), 1111–1120. https://doi.org/10.1086/421051
• Mathieson, I., Lazaridis, I., Rohland, N., Mallick, S., Patterson, N., Roodenberg, S. A., … Reich, D. (2015). Genome-wide patterns of selection in 230 ancient Eurasians. Nature, 528(7583), 499–503. https://doi.org/10.1038/nature16152
• Malmström, H., Linderholm, A., Lidén, K., Storå, J., Molnar, P., Holmlund, G., … Götherström, A. (2010). High frequency of lactose intolerance in a prehistoric hunter-gatherer population in northern Europe. BMC Evolutionary Biology, 10, 89. https://doi.org/10.1186/1471-2148-10-89

So, to answer your question, many dairying cultures never developed Europe’s high level of lactose tolerance because they never went through a phase where lactose tolerance became critical to survival. They had alternate sources of calories, so the ability to digest milk was never the bottleneck to survival or reproduction.