There is no such peerage.
There may be a connection with the Mormaerdom of LennoX, which went extinct in the 15th century, but it seems to be tenuous at best. The revived Earldom/Dukedom of Lennox (it was re-created four times, and finally promoted) belonged to the House of Stewart. The title was revived again a fifth time and made a subsidiary of the Duchy of Richmond, for Charles, the illegitimate son of Charles II (Stuart) of England and his mistress Louise de Kérouaille, Duchess of Portsmouth, and his heirs.
There is, or was, a Baronage of Lennoch held by the Drummond family, but there is no evidence that any member of this lineage ever settled in Virginia. (There seem to have been times when the title barely survived by one male heir - and of course no such heir would be going to America as a common colonist.)