lodash debounce not working in anonymous function

As Palpatim explained, the reason lies in the fact that _.debounce(...) returns a function, which when invoked does its magic.

Therefore in your #anonFunction example, you have a key listener, which when invoked does nothing but return a function to the invoker, which does nothing with the return values from the event listener.

This is a snippet of the _.debounce(...) definition:

_.debounce
function (func, wait, immediate) {
    var timeout;
    return function() {
      var context = this, args = arguments;
      var later = function() {
        timeout = null;
        if (!immediate) func.apply(context, args);
      };
      if (immediate && !timeout) func.apply(context, args);
      clearTimeout(timeout);
      timeout = setTimeout(later, wait);
    };
  } 

Your key event listener must invoke the returned function from _.debounce(...), or you can do as in your non-anonymous example and use the returned function from the _.debounce(...) call as your event listener.

Think easier

_.debounce returns a debounced function! So instead of thinking in terms of

$el.on('keyup'), function(){
   _.debounce(doYourThing,500); //uh I want to debounce this
}

you rather call the debounced function instead

var doYourThingDebounced = _.debounce(doYourThing, 500); //YES, this will always be debounced

$el.on('keyup', doYourThingDebounced);