Yes, except that you don't gain tolerance simply from continuing to drink milk. It's a regional evolutionary change from many generations continuing to drink milk and the majority of adults across the globe are actually lactose intolerant.
Worldwide, around 65% of adults are affected by lactose malabsorption. Other mammals usually lose the ability to digest lactose after weaning. Lactose intolerance is the ancestral state of all humans before the recent evolution of lactase persistence in some populations, which extends lactose tolerance into adulthood.
(Lactase is the enzyme for breaking down lactose.)
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