How do you know if the current element is not the first-child?
It should work with $(this), for example:
$(\"li\").click(function(e) {
          
        Check the index
$(this).index() == 0 // is first
You could simply ask for its .index() position (relative to its siblings).
$(this).index();   // returns a zero based index position
You can do this just to test an element if it's the first child: $(this).is(':first-child'). Other selectors like :last-child would work too.
Keep it simple, use the DOM
$("li").click(function(e) {
    if (this.previousSibling != null)
    {
        /* do something */
    }
});