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);

debounce doesn't execute the function, it returns a function with the debounciness built into it.

Returns (Function): Returns the new debounced function.

So your #function handler is actually doing the Right Thing, by returning a function to be used by jQuery as a keyup handler. To fix your #noReturnAnonFunction example, you could simply execute the debounced function in the context of your function:

$('#noReturnAnonFunction').on('keyup', function () {
    _.debounce(debounceIt, 500, false)(); // Immediately executes
});

But that's introducing a needless anonymous function wrapper around your debounce.

You can return the debounce function like this:

(function(){
    var debounce = _.debounce(fireServerEvent, 500, false);

    $('#anonFunction').on('keyup', function () {
        //clear textfield
        $('#output').append('clearNotifications<br/>');
        return debounce();
    });

    function fireServerEvent(){
        $('#output').append('serverEvent<br/>');
    }
})();

Came across this while looking for a solution to calling a debounce with a trailing call, found this article which really helped me: https://newbedev.com/lodash-debounce-not-working-in-react specifically:

Solution for those who came here because throttle / debounce doesn't work >with FunctionComponent - you need to store debounced function via useRef():

export const ComponentName = (value = null) => {
  const [inputValue, setInputValue] = useState(value);

  const setServicesValue = value => Services.setValue(value);

  const setServicesValueDebounced = useRef(_.debounce(setServicesValue, 1000));

  const handleChange = ({ currentTarget: { value } }) => {
    setInputValue(value);
    setServicesValueDebounced.current(value);
  };

  return <input onChange={handleChange} value={inputValue} />;
};

More generally, if you want a debounce with a trailing behaviour (accounts for last click, or more likely last change on a select input), and a visual feedback on first click/change, you are faced with the same issue.

This does not work:

$(document).on('change', "#select", function() {
    $('.ajax-loader').show();
    _.debounce(processSelectChange, 1000);
});

This would be a solution:

$(document).on('change', "#select", function() {
    $('.ajax-loader').show();
});
$(document).on('change', "#select", _.debounce(processSelectChange, 1000));