If you search for Viscount Thomas Arthur Southwell a Wikipedia entry - using Debrett's peerage as reference says he was the oldest son of Thomas Southwell, 1st Viscount Southwell and his wife Margaret Hamilton, daughter of Arthur Cecil Hamilton of Castle Hamilton, Killeshandra Co. Cavan.
Thomas Arthur Southwell 2nd Viscount Southwell, married 1774, to Sophia Maria Josepha Walsh, third daughter of Francis Joseph Walsh, Comte de Serrant, and they had four sons and four daughters (which aren't named) apart from the eldest son Thomas who became the 3rd Viscount on his father's death.
Do documents in Australia give Mary and Eliza's parents names?