The most common need I've found for some kind of locking mechanism in JavaScript is the very basic example of asynchronous functions triggered by UI. For example, button -> http call -> navigate. If the user presses the button twice, the call is made twice before navigating, which has unexpected results in some cases.

The lock in this case could be as simple as disabling the button as soon as the user clicks on it, but I've also find Promise-based locking functions to be very useful in solving these kind of problems.

I wouldn't call these "primitives" though - you don't need a language construct for it. It's easy enough to build the locks as functions working with Promises.