Add user managable titles to custom menus?

Are you looking to put a title on the nav links? That is built into the Menu feature in WordPress.

But this applies to the tag and not the <li> as you specified. You can, however, apply a class to the <li> by clicking the “Screen Options” link while in the Menu Admin page. Then, find the “CSS Class” checkbox under “Show advanced menu properties”.

Finally, you could give your links the desired title and then apply the following jQuery to apply the title to the <li> and remove it from the <a>.

$(function() {

    $('ul li').each(function() {

        var linkTitle = $(this).find('a').attr('title'); //get the link title
        $(this).attr('title', linkTitle); //apply the title to the li

        $(this).find('a').removeAttr('title');
    });

});

JSFiddle example: http://jsfiddle.net/tmort/E5VzC/3/