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.
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.
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".
Ralph Neville, 3rd Earl of Westmorland
Ralph Neville, 3rd Earl of Westmorland( c. 1456 – 6 February 1499) was an English peer.
He was the grandfather of Ralph Neville, 4th Earl of Westmorland.
John Stewart, 3rd Earl of Lennox
John Stewart, 3rd Earl of Lennox (c. 14904
September 1526,
Linlithgow, West Lothian) was a prominent Scottish magnate.
He was the son of Matthew Stewart, 2nd Earl of Lennox and Lady Elizabeth Hamilton, daughter of James Hamilton, 1st Lord Hamilton and Mary Stewart, Princess of Scotland, daughter of King James II of Scotland.
The Earl of Lennox led an army to Linlithgow with the intention of liberating the young King James V of Scotland from the pro-English Douglases.
He was defeated by a smaller force led by James Hamilton, 1st Earl of Arran, at the Battle of Linlithgow Bridge.
He survived the battle and was taken captive, only to be subsequently murdered by James Hamilton of Finnart.
Lennox was succeeded by his son, Matthew Stewart, the father of Henry Stewart, Lord Darnley, and the grandfather of King James VI of Scotland.
Margaret Douglas
Margaret Douglas, Countess of Lennox( 7 October 1515 – 7 March 1578), was the daughter of the Scottish queen dowager Margaret Tudor and her second husband Archibald Douglas, 6th Earl of Angus.
In her youth she was high in the favour of her uncle, Henry VIII of England, but twice incurred the King's anger, first for her unauthorised engagement to Lord Thomas Howard, who died in the Tower of London in 1537 because of his misalliance with her, and again in 1540 for an affair with Thomas Howard's nephew Sir Charles Howard, the brother of Henry's wife Catherine Howard.
On 6 July 1544, she married Matthew Stewart, 4th Earl of Lennox, one of Scotland's leading noblemen.
Her son Henry Stuart, Lord Darnley, married Mary, Queen of Scots, and was the father of James VI and I.
Henry Stuart, Lord Darnley
Henry Stuart (or Stewart), Duke of Albany (7 December 1545 – 10 February 1567), styled as Lord Darnley until 1565, was king consort of Scotland from 1565 until his murder at Kirk o' Field in 1567.
Many contemporary narratives describing his life and death refer to him as Lord Darnley, his title as heir apparent to the Earldom of Lennox, and it is by this appellation that he is now generally known.
He was the second but eldest surviving son of Matthew Stewart, 4th Earl of Lennox, and his wife Lady Margaret Douglas.
Darnley's maternal grandparents were Archibald Douglas, 6th Earl of Angus, and Margaret, daughter of Henry VII of England and widow of James IV of Scotland.
He was a first cousin and the second husband of Mary, Queen of Scots, and was the father of her son James VI of Scotland, who succeeded Elizabeth I of England as James I.
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:
John Stewart, 4th Earl of Atholl
John Stewart, 4th Earl of Atholl( died 25 April 1579) was a Scottish noble.
He was favoured by Mary, Queen of Scots, but later turned against her.
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 grandfather of Matthew Stewart, 4Th Earl Of Lennox?
Answer: Matthew Stewart, 2nd Earl of Lennox