Outlook 2013 and Lync 2013 suddenly cannot run at the same time

We recently switched to Office 365 and up until this month's Tuesday Patch Day, everything was working great. As soon as I installed the patches from 3/12/2013. Ever since then I've had the following issue:

1. Launch Outlook 2013
2. Launch Lync 2013
3. Get the following dialog box: "Outlook Data File: The file <filename> is in use and cannot be accessed. Close any application that is using this file, and then try again. You might need to restart your computer."
4. Click Ok to dismiss the dialog box. Everything seems to function normally.
5. About three minutes later I get the following dialog box: "We're sorry, but Outlook has run into an error that is preventing it from working correctly. Outlook will need to be closed as a result. Would you like us to repair now?"
6. Click Close. Everything seems to function normally.

Steps taken to attempt to a fix:

1. I deleted the Outlook profile and recreated it from scratch. No improvement.
2. I rebooted the machine. No improvement.
3. I repaired the Outlook data file. No improvement.

Other notes:

1. If I start Outlook 2013 by itself, it works fine and no dialog boxes.
2. If I start Lync 2013 by itself, it works fine and no dialog boxes.