Can you change the storage location of Conversation History for Mac Lync?
How about moving that directory to Drop Box, or a similar cloud-synced space, and then symlinked that path to your cloud directory?

You can create the link with the Finder 'Make Alias' command under File, or use Terminal to create a link with 'ln'.

The original directory goes in your cloud directory, and the alias goes back in /Users//Documents/Microsoft User Data/

This process is standard for DropBox, I assume it would work with other services too.