Yes Catherine II (the Great) did have a 'lady-in-waiting' of Scottish extraction.
An earlier post refers to General Patrick Gordon - a general in the army of Peter I. Peter the Great's closest friend, after Menshikov, was a Scotsman - James Bruce - another Scottish mercenery. When Peter was a teenager, Bruce rescued him from drowning when his little boat overturned in a river/canal near Ismailovskaya. From that day, for the rest of his life, Bruce was one of Peter's closest personal friends.
It was one of his descendants, or perhaps she was married to one of his descendants, (Margaret, I think) Brusova who was at the court of Catherine II. She was one of two impreuvesses. The doctor who minstered to Catherine and who was with her at her death was the Scot, Dr Rogerson from Dumfriesshire.
The Brusov estate lies north of Moscow and indeed the land became home to Russia's first golf course.
tsaria
PS: General Patrick Gordon died in the arms of Peter I. Nobody knew, more than Peter the extent to which Gordon was responsible for his victories.