Hi Cranstone,
Father Joseph Lambert seems to have died in 1907 and Mother Agnes in 1909.
Josephine seems to have been taken in by Uncle Tom Lambert. Horace and Frank were with Agnes, husband and children. Joseph the eldest was pursuing a military career.
I did find that Eric Arthur Willison born 1904 (son of Frank's sister Agnes Lambert and Arthur Ernest Willison) died in British Columbia 31 st May 1968.
Eric was married to Inez Erickson.
https://familysearch.org/pal:/MM9.1.1/FLBZ-Z2LLooking for immigration record for him, came across a Canadian Passenger List Avonmouth. England to Quebec on the Sicilian, arriving 10 September 1919. The Willison Family appeared - Agnes aged adult, Arthur 43 years, Arthur E aged 15 years, Austin aged 11 years, James 10 years and Harold 7 years. All travelling to a Mr Wood - Sifton. Manitoba.
Arthur was a Metal Worker but intended occupation was farming.
Sandra