Number the menu divs: rsbmenu$menuid and, lsbmenu$menuid, etc.
New menu item newitemrsmenu$menuid etc
Replace entire div after new item input.

On original load build an empty new menu x div with a new item section.
After name supplied, replace the x div with numbered div and include new x div.

Update:

Scratch all of the above. Was taking too long to program as AJAX functions so went in and did it with the old cgi coding method. Works fine for this kind of stuff.