Getting JSON with jQuery and creating lists with click events calling more jQuery and JSON
Two small nickpicks at the start: 


Empty HTML lists (ul, ol) are strictly spoken invalid. They should contain at least one list item. That said, I believe there is no browser limitation or other technical reason an empty list shouldn't work.
It is custom for the names of functions, variables and object fields in JavaScript to be written with a small letter at the beginning.


You can optimize adding the list item to the list, by using .map() to create the items and appending them all at once. 

$('#VerticalMenu') 
  .append(
    $(sections).map(function () {
      $('&lt;li/&gt;') 
      // ...
    })
  );


BTW, since sections is an array of simple JavaScript objects and not DOM objects it's a bit weird to wrap them in a jQuery object ($(sections).each(...)), because jQuery unwraps them immediately anyway. You should use $.each(sections, ... ) (or $.map(sections, ... )) instead.

You are assigning all items in your lists the same class (Section and SubSection respectively). Unless you remove the class later, this is usually a sign of wrong CSS design. If you leave out the class, then instead of the selector .Section { ... } you can use a descendent selector: #VerticalMenu li { ... }.

One last thing: The use of h4 elements seems wrong to me. Either this is a menu, then you shouldn't be using header elements at all, or the items in AccordionMenu are subheadlines and be using h5 instead.