After Lollipop - when I add account there isn't an option to sync contacts/calenders - only email
I had this same issue.  I had to delete the account and do the manual setup instead of the automatic installation using m.outlook.com as the server name.  Once this was done it gave me the options to sync contacts, calendars, etc.  Before that on the automatic setup it was only giving me the option to sync email.

Hope this helps if you didn't get it working by now.  Odd thing was that mine just recently started doing this it wasn't right after the Lollipop upgrade.  So no idea why it started.