Sussex Genealogies (Lewes Centre) (found in Horsham Library, Sussex) gives: p.159-160Lewknor of Kingston Bowsey.The third generation is Edward Lewkenor of Kingston Bowsey.Exor to fr 1522.Deft in fine for manor of Preston 1525.D.7 July 1528.Will dt 1 Oct 1527.pd 7 Nov 1528.(PCC 39 Porch).Inq PM 10 Apr 1529 (Chancy 47.41)Held manors of Ham, Parham and Hamsey.Md Margaret dau of Sir Roger Copley of Roughey.(Exex to husband 1528).Had issue: 1.Edward Lewkenor 2.Anthony Lewkenor.Named in fr's. will. 3.Eleanor.Named in fr's will.Md ... St.Barbe. 4.Mary.Named in fr's will.Bd at Horsham 30 Jan 1603/4.Md 1stly, John Michell of Stamerham, Gent.2ndly, as his 2nd wife, John Apsley of Thakenham. 5.Barbara.Named in fr's. will.Md Sir John Dawtrey, Kt.
This Barbara could be of the right age for your Barbara, living in the right county, with two marriages.Good luck.