I don't think Margery Lawrence & William Lawrence, Esq., of St. Ives are the correct parents for William Lawrence of St. Albans, Hertfordshire who married Katherine Lawrence and were parents of John Lawrence who married Elizabeth Bull and Margaret Roberts.
In "The Magna charta barons and their American descendants ..." his father is listed as John Lawrence of St Albans Hertfordshire with his mother unknown, his grandparents are Eleanor __ & Edmund Lawrence of Withington parish, Gloucestershire.