Some people who have upgraded to OSX 10.9 (Mavericks) are reporting issues while using Apple Mail to read LionMail. Symptoms include verification of the device password and mail syncing issues.
If you use Apple Mail to read LionMail, you might consider either waiting to upgrade to Mavericks or, if you choose to upgrade, use the web browser option for accessing LionMail (lionmail.columbia.edu) as an alternative. You can find more information on this web site: http://tidbits.com/article/14219
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