While I am writing this from the office, without my reference books at hand, my recollection is that different Scott families have arms that are quite dissimilar from those of Buccleuch. The common feature is that they display two mullets (stars) and a crescent, but there is little else that they share.
It is highly probable that EagleJCS does not belong to the duke’s family. There are plenty other perfectly respectable Scott families. He might be related to one of those that already bear arms, or on the other hand he may be unable to prove a connection. In this instance, Lyon would start afresh. EagleJCS might also want to start afresh, with or without reference to Lyon.
Regards,
Mike