CM12 (current self-built nightly) running on Moto G (falcon) here - unfortunately, DAVdroid stopped working for me after I updated both Android (5.0.2) and EGroupware (14.2). I used to run this setup (using older versions) for a long time and did not expect any problems. The new EGroupware version syncs fine with Lightning, etc. - this is why I suspect the problem may be DAVdroid on Android 5.
To rule out any problems in the F-Droid build I use I have built master for testing. CM privacy guard is disabled for DAVdroid. The setup process runs fine without errors (it also detects calendars and addressbooks). Also, DAVdroid does not throw any errors afterwards. I could not find any uncommon log entries, just the usual URL probing - the last thing I see is
I/davdroid.LocalCalendar( 9452): Inserting calendar: calendar_color=-3937682 canOrganizerRespond=1 sync_events=1 ownerAccount=testuser canModifyTimeZone=1 visible=1 account_type=bitfire.at.davdroid allowedAttendeeTypes=0,2,1,3 allowedAvailability=0,1,2 name=https://example.org/egroupware/groupdav.php/testuser/calendar/ allowedReminders=1 calendar_timezone=Europe/Berlin account_name=testuser calendar_access_level=700 calendar_displayName=Kalender Testnutzer -> content://email@example.com&account_type=bitfire.at.davdroid&caller_is_syncadapter=true
It does not sync any calendar or contact entries afterwards. Nothing in the logs, neither server nor logcat. Let me know if I should post full logcat. I would be glad about any hints - starting with, if I should open a seperate issue for this.