'The Lawn', Hicksey Hill

[Eldon]

William Henry FLOWER married Eliza HICKS in Liverpool and raised a family of four. They appear on the 1891 census and the 1901 census has William as a widower.

I have trawled the National death register and find that William Henry Flower died 1933 and was a retied farmer at The Lawn , Hinksey Hill., His son William Henry Flower died in 1965 and was also a retired farmer at The Lawn. His daughter Esther Regina Flower a retired secretary died in 1963 and she also lived at The Lawn. Another daughter Eliza Catherine Flower (who was their informants) also lived at The Lawn and she died in 1981 at another address. I have travelled along Hinksey Hill but could not find 'The Lawn'
I have searched the South Hinksey Church Cemetery and cannot find their headstone(s). The Flower family had a very strong dissenting upbringing so I was not really surprised.

Does anyboby know whether 'The Lawn' still exists?
Which public cemetery would they be buried at? I am aware that Hinksey Hill is on the border of Berkshire with Oxford, and I would assume that they were buried in Berkshire. (The 1933 death cert. has Hinksey Hill in Berks while the later certs have it in Oxford.)

Thank you ...Eldon