If you upload your site to the Lunar Pages server, but leave your site up on your present server for a while, then you can change the DNS numbers and the change will be seamless.  As the new DNS numbers propogate, more and more of your mail will come to the Lunar Pages server, but you won't lose any mail in the meantime, because you'll still have access to the old server.  I did this recently, and had no trouble.  I was downloading mail off two different servers for the same web site for about a week, but I didn't lose a thing.

Eliz.  

While probagation, your mail will reach either servers which is uncertain. At this time (2-3 days) check all your mails with web base email from your control panel in both web hosts.

If you check with your email client (outlook, eudora...) you will probably checking mails from 1 server and you won't see mails in another server.