Microsoft Transporter Suite, and Lotus Domino

Not sure what you mean by "see it in the first place." The AD part of it doesn't touch a mailbox, it reads the Domino Directory. I assume "X" and "mail" are the same name? And they refer to the Domino mail If server, not an Exchange host name?

you run the Notes client on the box you are using for mailbox migration, you should be able to verify Notes connectivity to the named server. There is a tool built into the client's network preferences section to test connectivity, and it indicates whether it succeeded in resolving the name, what it resolved the name to, and whether it and how it succeeded in communicating with the server using that resolution, and any secondary path(s) it tried upon failure.

Lotus notes can connect on the machine that is doing the migration.

Yes the name of our Lotus Domino server is Mail.

I can migrate users, but when I try to migrate mailboxes from Lotus to Exchange, that's where I get the error.

The manual basically had all the answers.  I had to go through it with a fine toothed comb.  I also looked at various walk throughs on line.