Alexander, son of the Earl of Mar, was Anna’s cousin and the subject of the song, Lady Bothwell’s Lament.

According to the Erskine website, he was blown up at Dunglas house, East Lothian with his brother-in-law the Earl of Haddington 30 Aug. 1640. Alexander had issue a natural son Alexander by Anne Bothwell, daughter of the first Lord Holyroodhouse. At the Reformation the possessions of the canons of Holyrood in Leith were bestowed by James VI on John Bothwell, who stood high in royal favour, and his indulgent master at the same time created him Lord Holyroodhouse. [King James VI was Alexander Erskine's father's best friend]

This appears to be the Anne Bothwell referred to in the song, Lady Bothwell’s Lament. However, she is the granddaughter rather than the daughter of the Bishop of Orkney. She bore Erskine a son, under promise of marriage, but was deserted when he was killed.

Anna was the executrix of her father’s estate.

The theme of Lady Bothwell’s Lament was also used in: Intermezzi, Opus 117, No. 1, 2, 3 (1892) by Johannes Brahms