Does a LID user have to have exclusive control over a web server, or a DNS domain?
No. For security reasons, it is advantageous to make sure other users of a server cannot access one’s LID installation, which may be accomplished easiest on those servers over which one has exclusive control. However, there is no reason whatsoever why a service provider, for example, couldn’t host thousands of LID URLs on the same server, using the same or different domain names.