I am very sorry, It appears you have been trapped by localized usage. It appears the term is almost useless, except for local definition/identification.
From AGI Dictionary of Geological Terms:
Lutite, A general name for rocks composed of material that was once mud, e.g. shale, mudstone, calcilutite.
I can't do any better using my Petrology Texts.
Using the Geological Nomenclature, Royal Geological & Mining Society of the Netherlands, 1959,
Lutite, any rock composed of fine particles of silt or clay.