Where is the coffee shop on back lot island?

You have to get two smaller coffees of different types and mix them.

At the first Queequeg's (next to the Talent Agency), they are out of Lattes. Get an infant espresso full caf. At the second shop, they have no Espresso, so get an infant latte decaf. Select either of the two from your items and you will be prompted to mix them into the empty Leviathan cup, where they mix to form a half-caf latte-espresso that you need.

* You can also get "Infant Espresso Decaf" and "Infant Latte Full Caf" - these will mix the same way. As long as one is decaf and the other full caf, it works.