I'm hearing two entirely different things here:
and

Well, either it is or it isn't. Some hosting companies offer package deals where they control the domain registration too, so if you want to leave and take your domain elsewhere, they can make it a very painful experience. They may even retain ownership of the domain name in the fine print. On the other hand, if you have the domain name registered with someone completely different than the hosting company (always a good idea), you are free to point your domain to another hosting service at any time. Sure, your friend will lose the balance on the unused portion of the service term if they walk away (unless they use it to put up another site temporarily, such as http://XYZHostingServiceSucks.com), but they should be free to move to another host.

If your friend wants to come to LP, they sign up for a hosting account and load up their site using http://servername/~accountname. Double check with LP when they sign up, but that should be quite possible. Then they go to their domain registrar and update the nameserver(s) the name points to, and within a day or two everyone in the world is looking at the LP-based site. The only fly in in the ointment is whether they require a seamless transition to the new site. During the cutover, DNS servers around the world will point to the old site for a short time, and won't switch over simultaneously. You could end up with customers visiting the old site and buying things there, etc. That problem might be solved by putting a "URL redirect" on the old site to send them to the new one. If they don't mind a day or two of down time, they can turn out the lights on the old site just before they change their domain name pointing, and leave a message to customers to try again in a day or two. Once the entire DNS finishes updating, no one will be sent to the old site.