My avast! antivirus software is identifying two Trojan viruses on my MacBookPro (Max OSX 10.7.5) that seem to be related to my Outlook for Mac. An example of one of the file names is: /.MobileBackups/Computer/2014-06-22-151618/Volume/Us

You don't need Avast for that, or any other AV software. Also, a Trojan and a virus are not the same thing. They are two different types of malware.

Anyway, you simply have some garbage attachments in a couple of emails you received. It's a virtual 100% probability they are Windows malware of some sort and can't do a thing to OS X. Just delete the emails they're in.

Actually, you can delete the entire Main Identity folder for Outlook that has a backup date in brackets [xxx] as part of its name since that was created when you used the Microsoft Database Utility to rebuild your email database. The folder that is only named Main Identity is the one in use. The other is now nothing.

Uninstall Avast. It is notorious for identifying false positives. "Trojan virus" is a meaningless contradiction in terms and the files it identified as such are either completely innocuous or Windows malware that has no effect on a Mac.

Avast is capable of nothing beneficial. Its uninstaller will remove all traces of its existence, having taken nothing but your time and / or money and leaving nothing but the bad memory of having wasted both.

Follow its uninstallation instructions.

The filename is not nearly as important as the name of the malware. What malware does Avast say it has found?

Most likely, this is Windows malware and cannot possibly infect your Mac. The file that was found is located in your hidden MobileBackups folder. Time Machine maintains a set of backups on your internal hard drive for one week, so that you can recover files that are inadvertently lost or destroyed while you're away from your normal backups. That file is completely inert, not capable of infecting you even if it's Mac malware, and will be automatically deleted on the 29th.

I would concur with the others... Avast is more trouble than it's worth. Get rid of it. But first, figure out whether what was found is supposedly Mac malware or not.

Actually, you can delete the entire Main Identity folder for Outlook that has a backup date in brackets [xxx] as part of its name since that was created when you used the Microsoft Database Utility to rebuild your email database. The folder that is only named Main Identity is the one in use. The other is now nothing.

That should be true but sometimes users are in the wrong Identity. Outlook 'forgets' what is supposed to be the main default Identity and opens in the wrong one. You need to check the database file in the Identity to see date modified to know for sure.

Typically, after rebuilding you delete the rebuild after a bit when you are satisfied with the rebuild. There should only be one Identity in the Identities folder. However, most users don't understand what to do with the copy that is made and never deletes anything.