I'm using Ubuntu 16.04 dev and on my laptop and my desktop PC I have the same version of lxdm installed ( 0.5.3-1 ). On executing "dpkg -S /etc/init/lxdm.conf" on my laptop it shows "lxdm: /etc/init/lxdm.conf" but on my PC it shows "dpkg-query: no path found matching pattern /etc/init/lxdm.conf". This means that I have fetched in the past 2 times the package lxdm 0.5.3-1 with different content in it.
I have noticed this discrepancy as I have today purged for a test lxdm on my desktop PC and reinstalled it later. On rebooting my PC lxdm hasn't started automatically anymore (manually executing "/etc/init.d/lxdm" does solve this issue but I'm not sure if this is another bug (I'm still using upstart)).
I have figured out something new: On my laptop I have executed "apt-get install lxdm --reinstall" to update the lxdm package. But after executing "dpkg -S /etc/init/lxdm.conf" again I got again a match for lxdm on this path. On checking the package with "apt-get download lxdm" the file doesn't exist there. This means dpkg has not correctly updated the package by cleaning up this obsolete configuration file. Now I do even think that this issue is not about lxdm but maybe dpkg is just causing migration issues.
Taking care of obsolete conffiles is a responsibility of the package, not dpkg.
I have tested this by creating 2 versions of a package where the first creates the configuration file /etc/test/test1.conf (test1.deb) and the second creates the configuration file /etc/test/test2.conf (test2.deb). On installing test1.deb and then test2.deb only the file /etc/test/test2.conf exists so dpkg does clean up obsolete configuration files. But it seems this does not happen if a package gets reinstalled as sayed in comment #1.