Children in their 60's does sound rather unlikely but according to the two records that I have, it appears to be fact.
His 1946 death certificate lists all of his children. The last child is recorded as Halyn Eyre Lucas, 8 years.
The 1945 Tennyson State School register records Halyn Eyre, 7 years 1 month, DOB: 22.1.37.
He was not divorced from his first wife, so there shouldn't be any marriage record with Lucas.
If Lucas remarried following Harry's death, that makes it all the more difficult to trace her.
I don't know whether Halyn might have used the name Eyre or Lucas.
....and I don't know where they might have met. He may well have met her in NSW and then re-located to QLD.
This may well be a brick wall that I won't be able to penetrate. 
No-one is doubting that Harry is the father of Halyn - Charlie Chaplin was still having children in his 80s. Women, however, very rarely have children naturally conceived, after the age of 50.
Your original query was to find him and BL on the electoral roll - I believe BL has been FOUND, but you seem to think not.
.Beryl Llewellyn (initials B L) Lucas was born in Victoria in 1898.
.Some of her biography has been provided on a link from Sue.
.She is 23 years younger than Harry, which fits in with your prior information.
.In 1919 and 1824 she is on the electoral roll in Victoria.
.In 1936 she is on the electoral roll in Qld living with Harry Eyre Lucas. If Harry has left his wife to live with B L, he may well have been recorded with the same surname as her. He may not want his wife to find him. He may not want the neighbours to know they are not married.
. In 1937 per your information, they have a child.
. In 1945 The school registers name the father. It was probably common for the registers to list the next of kin - usually the father - unless he had passed away.
. In 1967 B L dies and is buried in Brisbane with her mother. She is buried under the name of Eyre.
The main query would be whether or not B L and Harry married - she may have simply taken his name, changed it by deed poll, or if the first wife had died, she may have married him.
I really don't know why you think this is a brick wall. Do you have some definite proof that
Beryl Llewellyn is not the BL Lucas you are searching for?
Trish