Charles Stuart, 1st Baron Stuart de Rothesay
Charles Stuart, 1st Baron Stuart de Rothesay (2 January 1779 – 6 November 1845), known as Sir Charles Stuart between 1812 and 1828, was a British diplomat.
He was twice Ambassador to France and also served as Ambassador to Russia between 1841 and 1844.
Charles Stuart, 1st Earl of Lennox
Charles Stuart, 1st (or 5th) Earl of Lennox (April or May 1557 – April 1576), was the fourth son of Matthew Stewart, 4th Earl of Lennox and Margaret Douglas, daughter of Margaret Tudor and granddaughter of King Henry VII of England.
His brother was Henry Stuart, Lord Darnley.
Elizabeth Stuart, Countess of Lennox
Elizabeth Stuart, Countess of Lennox née Cavendish (31 March 1555 – 16 January 1582) was an English noblewoman and the wife of Charles Stuart, 1st Earl of Lennox.
She was the mother of Arbella Stuart, a close claimant to the English and Scottish thrones.
Margaret, Countess of Lennox
Margaret, Countess of Lennox was the daughter of Domhnall, Earl of Lennox, who died in about 1364.
She married Walter de Fasselane, a cousin, who also descended from previous Earls of Lennox.
Margaret and Walter's children were:
Esmé Stewart, 1st Duke of Lennox
Esmé Stewart, 1st Duke of Lennox, 1st Earl of Lennox( 154226 May 1583) was the son of John Stewart, 5th Lord of Aubigny, who was the younger brother of Matthew Stewart, 4th Earl of Lennox, and his wife Anne de la Queuille.
Sir James Melville described him as" of nature, upright, just, and gentle".
Robert Stewart, 1st Earl of March
Robert Stewart, 1st Earl of Lennox then 1st Earl of March( c. 152229 March 1586) was a Scottish nobleman of the family of Stewart of Darnley.
Matthew Stewart, 4th Earl of Lennox
Matthew Stewart, 4th Earl of Lennox (21 September 15164 September 1571), was the fourth Earl of Lennox, and a leader of the Catholic nobility in Scotland.
He was the son of John Stewart, 3rd Earl of Lennox and Lady Elizabeth Stewart, daughter of John Stewart, 1st Earl of Atholl.
His grandson was King James VI of Scotland and I of England.
Margaret de Stafford
Margaret Stafford( born c. 1364; died 9 June 1396) was the daughter of Hugh de Stafford, 2nd Earl of Stafford, and Philippa de Beauchamp.
She was the first wife of Ralph Neville, 1st Earl of Westmorland, and the grandmother of the 2nd Earl.
James Stuart, 2nd Earl of Bute
James Stuart, 2nd Earl of Bute( before 1696 – 28 January 1723) was the son of James Stuart, 1st Earl of Bute and Agnes Mackenzie.
John Stewart, 1st Earl of Lennox
John Stewart, 1st Earl of Lennox( before 14308 Jul/ 11 Sep 1495) was known as Lord Darnley and later as the Earl of Lennox.

Question: Who is the paternal grandmother of Charles Stuart, 1St Earl Of Lennox?
Answer: Elizabeth Stewart