If I am not mistaken-which i often am but the Court of Lord Lyon has nothing officially to do with registering tartans-
The Court of the Lord Lyon is the heraldic authority for Scotland.
It deals with all matters relating to Scottish Heraldry and Coats of Arms and maintains the Scottish Public Registers of Arms and Genealogies.
The Lord Lyon King of Arms is also responsible for State Ceremonial in Scotland.

The Scottish Tartans Authority on the other hand maintains a registery of tartans-but getting it registered does not offer any copyright or trademark protection.