Added: Getting a red flash with your post Jon but will post this as is...
If we are following the same William Snr and family:
1894 Marriage for William Lawrence and Clara Jane Wilkins in Wandsworth 2nd Qrt
1894 Birth of a Dorothy
Louisa Lawrence in Brixton, mother's mn Wilkins - 1st Qrt
1901
www.familysearch.org/ark:/61903/1:1:X9N8-SRL - parents details match with 1911 but where are the other children

1911
www.familysearch.org/search/ark:/61903/1:1:XWWP-GJM1919 Marriage of a William H Lawrence to a Mary Johnson in Brentford 1st Qrt. Could this be a second marriage for William H C. Snr. Could this be the Mary, Widow, mentioned in Probate?
Death of Clara Lawrence? There is one in Brentford in 1915, but indexed as age 94

However, Jon, from your listing for 1920 there shows a Louisa and I am wondering if this is Dorothy Louisa from 1894? Which means this family is wrong

Monica