Thanks for the quick response Frank!
So I see various information on Family Search now.
So do you think the father would be Miles Herman Lawrence who was born 1856 in Tudeley, Kent, England. ( https://www.familysearch.org/tree/person/details/KJWB-5S8 )
I see another source lists his wife as Anne Jones. Looks like she immigrated to California about 1885.
Though on the Family Search profile for Miles Herman it lists father of Sir Thomas Lawrence 1769–1830 who would of been dead for 20+ years before Miles was born and who according to WikiTree did not marry or have issue: https://www.wikitree.com/wiki/Lawrence-39
Thanks for your help! Helping my friend Nils research his family tree.
Allowing for a bit of variability in the year of birth, there were 16 people called Sydney Lawrence with births registered in England between 1878 and 1882. There were also another 18 people called Sidney Lawrence with births registered in that time period.
However, the 1940 census on his profile says he was living in Portland, Oregon at that time, so I assume that his WWII draft card is the one at https://www.familysearch.org/ark:/61903/1:1:QVJT-RZ2T. That says he was born on 26 November 1879 in Broad Clyst, Devon, so his birth registration is the one Hilary Gadsby stated in her answer (https://www.familysearch.org/ark:/61903/1:1:2XNK-N8Z), as the St Thomas registration district is the one that covers Broad Clyst (see https://www.ukbmd.org.uk/reg/districts/st%20thomas.html). As Hilary says, his mother's maiden name from the GRO website is Hancock.
It seems likely that this is him in the 1881 census with his parents William B. Lawrence and Catherine - https://www.familysearch.org/ark:/61903/1:1:Q276-P7NT
This looks to be his parents marriage in 1867, when William Bastone Lawrence married Catherine Hancock - https://www.familysearch.org/ark:/61903/1:1:2DK3-V2X