Lucy Burke is mentioned in the 1787 will of her father.

Lucy probably died sometime before her father, according to papers below from Burke vs. Chenault.

From undated loose papers from Burke vs. Chenault:
Thomas Burke died under age after his father John Burke in the year 1788 or 9—
John Burke died soon after the will was made—
John Burke left Rose, Isaac, Haris, Lidd, Sam, Moses, Peter, Reuben, Dicy & Rose has since had Abram & Liddy has since had Lucy
Lucy Burke is not mentioned in the decree for sale of the land speak to Mr Chenault & also which of the children are infants—
Mrs Burke renounces the will
[Essex County, Virginia, Box Chancery No. 32, 1823, paper 32-I-26.]

From undated petition in loose papers from Burke vs. Chenault:
John Burke died sometime about the year 1787, leaving Richd, Ann, Edmund, Susanna, Wm, Judith & Thomas Burke his only children. Will dated 12 Feb 1787. Will proved in 1788. Susanna his widow. [Essex County, Virginia, Box Chancery No. 32, 1823, paper 32-I-33.]