John, just another thought, a marriage certificate for Joseph Thomas Corkill Lace may reveal his dad's name and that would narrow down the search.
Are you aware of this record?
Marriage in the September quarter of 1939
Joseph T C Lace to Jane Bearsley Liverpool North 8b 949
Then there are 2 births that are possibilities for this couple in 1942 and 1945.
Sorry if you know all of this, you may have the marriage certificate already but for some reason the dad's name is not stated.
Ewan