This 2-minute tutorial explains how the Lunatics! characters should be linked into a shot file for animation. There are 6 steps outlined here:

1. Link the character group
2. Link the Rigify script for the character's armature
3. Link the Lunatics! face rig control script
4. Link desired Pose Libraries or Actions (especially the Phoneme Post Library)
5. Proxy the Armature (and other control objects if they exist)
6. Assign the Phoneme Pose Library to the Character Armature

[Erratum: the video says to assign the Pose Lib to the mesh, but it's actually associated with the armature]