Hi Your father William E. TOWE married Anita ? 1960/1970
If your father has the Marriage Certificate or the Birth Certificate for the child Lindsay TOWE - it would give you a start.
Was there a Divorce ? Death ?
Since your father is still living - he could / you could on his behalf - obtain the Marriage Registration - this has full information as required at the time - rather than the Certificate which only holds basic information taken from the Registration. Will show the Surname for Anita - as well her birthplace - names of her parents including maiden name of the mother.
Searching City Directory Henderson/ Wigleys - may show where the family were living at any particular time.