Hi Andrea,
This might help you get started.
Lawrence Lennox appears to have been born in 1901. He is shown, living at 262 Morrison Street in Edinburgh, aged 10 weeks old! The transcription I have suggests his Mother was 56 year old Jane Duncan Lennox but I imagine she was his Grandmother. She was certainly head of household but I would think William Lennox is more likely to be his Father with Helen his Mother. Details as follows;
Jane Duncan Lennox Head, Aged 56, No occupation
William Lennox Son, Aged 30, Grocer, Born Galashiels
Helen Lennox Daur-in-Law, Aged 28, Born Galashiels
Gracie Ann Lennox Daughter, Aged 25, Baker's Shop Assistant, Born Galashiels
John Duncan Lennox Son, Aged 23, Hewer Mason, Born Newbattle
James Lennox Son, Aged 20, Locomotive Fireman, Born Galashiels
Jane Lennox Daughter, Aged 17, Baker's Shop Assistant, Born Galashiels
Catherine Deas Lennox Daughter, Aged 11, Scholar, Born Galashiels
Lawrence Lennox Son, Aged 10 weeks, Born Edinburgh
From this you can use Kirsty's suggestion to use Scotland's People. Lawrence's birth certificate should be easy to find. I could track the various census records back for you but half the fun is in doing it yourself!
Let me know if there is anything else I can help with.
Happy Hunting and Regards,
Kenny