I can't find any sourced records that include Ann Lambert as a member of this Lambart family. Sources all have the following information;
The Peerage of Ireland, Vol 1 by John Lodge 1754
p. 358-9" Oliver Lambart, Esq, the third son of Charles, Earl of Cavan, was seated at Painstown, County Meath...dying 13 December 1700 was there buried. He married four wives, but had issue only by the two former who were Catherine Bridges [issue] & Eleanor Creane whom he married in January 1677...by her he had one son Charles and seven daughters...Charles Lambart of Painstown, Esq, the only son who died in September 1753, was for many years Member of Parliament for Kilbeggan, married Elizabeth, only daughter of Gustavus Hamilton, Lord Viscount Boyne, by who he had 4 sons and six daughters; Charles born October 1703,...died unmarried December 1740, Oliver died young, Gustavus, Collecter of the Port of Wicklow, and in Feb 1746 made collector of the district of Trim....Hamilton Elizabeth married to Nicholas Ogle 16 Feb 1754, Eleanor married to Thomas Elrigington, Mary married to Christopher Nicholson of Balrath, County Meath, Sophia married to Rev. Robert Gregory, Amelia who died suddenly 28 Nov 1755 and Frances Arabella who died an infant."
Assuming there is an Ann Lambert in Virginia, I suspect she does not belong here.
