I was able to get Outlook 2011 and Thunderbird working with mBox with Lion OS. The issue you are having seems to be a mBox compatibility issue with the Apple Mail program. I too have sent email to mBox, but there has not been an answer yet. So I download the free trial of Office.
To setup the account, enter in your email account/password then uncheck the "Configure automatically" box. You can then change the account type to IMAP and the server to localhost:9143 (no SSL) as is required by mBox and the outgoing server smtp.live.com:587 and use SSL to connect. In the Advanced settings, I checked "Send multiple commands to the server simultaneously" to speed up the sync process when the email is read. If you need more information, I think that the settings were similar to the FluentFactory mBox website instructions for setting up thunderbird.
There are still some syncing issues for me, but I can restart mBox easily to solve the issue.