It's his father William I'm trying to nail down.
His father was probably Edward Lindsey and his mother Ann Matfin, problem is the marriage says he married Elizabeth Matfin, her sister !!!
Not any help in finding William

and I don’t know if this Lindsay fits anywhere in your family tree but just in case....
Mary LINDSAYBorn 26/6/1804
Christening Date 19/6/1804 Newcastle Upon Tyne Northumberland
Father William LINDSAY mother Elizabeth
Maternal grandfather’s name Thomas
MATIN*added* - ah.... just seen this
William LINZEYbirth date 13/2/1802
Christening date 21/2/1802 Newcastle Upon Tyne
father Edward LINZEY mother Ann
Maternal grandfather's name Thomas
MATFIN