Hrhdiddy, using the Access to Information and Privacy (ATIP) procedure (use the formal request option) should work given that his name is likely unique. I assume you do not have his service number or birthdate to provide additional details.
One alternative, although its a more expensive than the ATIP request, is to use one of the freelance researchers listed by LAC. A researcher can work with the LAC staff to ensure the correct file is being drawn even when the full identification details that LAC prefers are not available. From my own experience with him, I can recommend Arnold Kay for this, he can be found in the LAC list of researchers at the following link.
Hiring a Freelance Researcher - https://www.bac-lac.gc.ca/eng/freelance-researchers/Pages/freelance-researchers.aspx
There is a John Lawrence Bavington listed in ancestry.ca
- BIRTH 8 OCTOBER 1927 %u2022 Toronto, Ontario
- DEATH 26 DECEMBER 2003 %u2022 Ottawa, Ontario
The page links to this grave record:
John L. Bavington in the Web: Canadian Headstone Index, 1840-2017
Name: John L. Bavington
Cemetery: Notre Dame - Section J
Burial Place: Carleton (incl. Ottawa), Ontario, Canada
Notes: BAVINGTON LEST WE FORGET JOHN L. BAVINGTON LIEUTENANT - RCAMC WORLD WAR II VETERAN AN OFFICER AND A GENTLEMAN OCTOBER 8, 1927 - DECEMBER 26, 2003 BELOVED HUSBAND OF JEANNE-MANCE LAFRANCE MARCH 30, 1926 -
Obituary: https://ottawacitizen.remembering.ca/obituary/john-bavington-1065879803
He appears here in the Canada Gazette:
Part I (1947-1997), volume 85, number 36, 8 September 1951, page 12
https://www.collectionscanada.gc.ca/databases/canada-gazette/001060-119.01-e.php?image_id_nbr=717007&document_id_nbr=11625&f=g
Royal Canadian Infantry Corps
TB14014 John Lawrence Bavington (Central Comd Cont, COTC) to be Lt., 30 Apr 1951