Connection to royalty?

David Lidderdale (1675 - 1732)  married Eleanora (about 1680 - 1757), eldest daughter of Sir James Dunbar, first baronet of Mochrum by his wife Isabel, daughter and co-heiress of Sir James Nicholson, Baronet of Carnock.
Eleanora was 10th in descent from James II of Scotland and 14th from Edward III, through her grandmother, Lady Margaret Livingstone, daughter of Alexander, second Earl of Linlithgow.

Sir James was 12th in descent from Robert II of Scotland, being descended from the Dunbars, former Earls of Dunbar, March and Moray.

Sir James, whose title was a creation of 29th March 1694, was a man of immense size, with a great sense of humour. When he died he had to be taken from his bedroom through a hole made in its wall.
http://www.lidderdale.com/gen069.html - David Lidderdale at Lidderdale.com

Scottish Monarchs - James II of Scotland (1437-1460) - http://www.englishmonarchs.co.uk/stewart_4.htm
Born 16 October 1430 and died 3 August 1460
King James was married to Mary of Gueldres on 3rd July, 1449 at Holyrood Abbey, Edinburgh. It was to be a happy marriage which produced seven children, including the future James III.

Scottish Monarchs - Robert II (1371-1390) - http://www.englishmonarchs.co.uk/stewart.htm
Born 2 March 1316 and died 19 April 1390
First wife was Elizabeth Mure of Rowallan, the daughter of Sir Adam Mure - they had ten children. They married in 1347 - all the children were born out of wedlock.
His second wife was Euphemia, daughter of Hugh, Earl of Ross - they also had children

Robert II was the grandson of Robert the Bruce who led his countrymen to battle to gain independence at the Battle of Brannockburn in 1314. He ruled Scotland until his death in 1329. His daughter, Marjorie, was the mother of the future King Robert II and his father was Walter, 6th High Steward of Scotland. - http://www.englishmonarchs.co.uk/bruce.htm

English Monarchs - Edward III (1327-77) - http://www.englishmonarchs.co.uk/plantagenet_7.htm
Born at Windsor Castle on 13th of November, 1312  and died 12th June, 1377
Married  his first cousin, Phillipa, on 24 January, 1328 and they had a large family

Obviously, as time permits, research is required to verify the 'royal connections'

Two sites that may be useful

Cracrofts Peerage - http://www.cracroftspeerage.co.uk/online/

The peerage.com - http://thepeerage.com