I have learned that liquids are uncountable, except for measurements such as "three cups of water."
So, does "three lattes" in this context refer to three cups of latte?
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This is a specific usage that concerns items on a menu. It is perfectly acceptable to say "three lattes" or "one water" because you are referring to a specific item like a bottle, rather than a substance.
In Australia, a few years ago, Kylie Minogue (aka 'The Singing Budgie') featured in a TV commercial for Coca Cola.
In the commercial, she ordered Two Coke, and this caused some public debate.
The answer came from the Coca Cola company itself, which I can summarise by saying Coke is a trademark and correct usage of the mark requires it to be both singular and plural — Owners of such valuable marks take these things very seriously.
But I'm not aware that anyone considers the word latte a trademark, so it should be safe to treat it as countable as jackgill described.
As a native American English speaker, I find "Three lattes for takeout. Is that all?" to be entirely grammatical and natural. Saying that all liquids are uncountable is an oversimplification of the actual rules for determining countability.