In the unpublished short story The Incident of the Dog's Ball, Dr Lawrence is the local doctor serving the village of Little Hemel in Kent and the regular doctor of the wealthy old lady Matilda Wheeler. He attended to her during her various illnesses and also after she fell down the stairs. Later when she died, he determined that she had died from natural causes through "yellow atrophy of the liver".
When Agatha Christie later expanded into the short story into the full length novel Dumb Witness, she inserted several Market Basing doctors into the story. The one with the role parallel to Lawrence is Dr Grainger. Both are about sixty years of age and both lost their sense of smell because of influenza.
However, as the short story has fewer characters, Lawrence has more roles than Grainger. He is the first person Poirot interviews. Lawrence provides background information on the Wheeler household and also some details of her will. He also tells Poirot that Miss Wheeler was of sound mind and perfectly capable of making her will (here Poirot never interviews her solicitor).
Hastings describes Lawrence as "an unambitious kindly sort of fellow, not particularly brilliant mentally, but quite sound."