Birth information in NSW for the period you are searching is not available. Online birth information extends to 1910 and another resource, to 1918.
The death certificate for either parent would give you details of any children.
Transcriptions of certificates are available in NSW - a cheaper and quicker option to purchasing a certified certificate.
http://www.bdm.nsw.gov.au/familyHistory/howToTraceYouFamTree.htm#TranscriptionAgentFuneral notice for Lawrence.
http://www.rootschat.com/links/0bc5/Lawrence and Rebecca are buried at Rookwood Catholic Cemetery however another source does not have a headstone listed for them.
http://www.catholiccemeteries.org.au/Rebecca was buried at Rookwood on 16 Nov 1966. A lookup in the newspaper of the day for a death notice, may hopefully detail the names of their children.
Australian Electoral Roll
1930
LINANE Lawrence, Daylesford, Sunbeam Avenue, Burwood Storeman
LINANE Rebecca Mary, Sunbeam Avenue, Burwood HD
Cheers

Cando