There is also this marriage in 1929:
John Scott Gateshead
Mary Snowdon Gateshead
As the Frank that I can see was born in 1930 (unless you mean a different birth) then he would look to be the son of John and Mary, not the son of Walter and Isabella, surely?
A free 1939 search gives Frank Scott, 1930, with a Mary Carroll/Scott and 1 other person in Gateshead. Lilian Scott, 1933, is also in that household.
So that explains the near births of Lilian and Walter - 2 different families.