You must have a My Domain org to use the Lightning Component.
To use the Lightning Component, the users in the org must have read permission to custom metadata types for Composer (and CQG) to read the refresh token stored there (this is in the Composer permission set).
All Composer packages older than version 8.179 "Grays" must provide explicit Read permissions for all Composer users to custom settings and metadata.
If an Admin installs the Conga Composer and selects "For Admins Only" during the installation, then they will need to create a permission set to give their users access to the connected apps and all Composer package components.
Composer_Administrator permission set.
Conga Batch Region Metadata permission is required to run Batch from Grid view.
To use the Lightning Component for SF1, you must have "Modify Metadata Through Metadata API Functions" AND "Customize Application".