They don't ship MIME settings for the .diary type, so xdg-mime has no idea what these files are.

It appears that it has the right stuff, but is 100% designed to be run and installed by a user (rather than with packaging).

cmake/xdg.cmake is a script to setup up the mimetype for the user, but it'll never be included in the package that way.

I looked at the included MIME file and it didn't even set a file extension..sooo

I don't know much about mime (nor do I want to), but that should do it

$ cat lifeograph.xml 
<?xml version="1.0" encoding="utf-8"?>
<mime-info xmlns='http://www.freedesktop.org/standards/shared-mime-info'>
  <mime-type type="application/x-lifeographdiary">
    <comment>Lifeograph diary</comment>
    <comment xml:lang="tr">Lifeograph günlüğü</comment>
    <magic priority="100">
      <match type="string" offset="0" value="LIFEOGRAPHDB\n"/>
    </magic>
    <glob pattern="*.diary"/>
  </mime-type>
</mime-info>