You aren't the only person to have lost him. Lorenzo Grove Chesterton was the son of Edward and Elizabeth Emma according to his baptism record.
On 21st July 1901 there was a personal ad in the Los Angeles Times on p20. Previously appeared on 17th and 19th.
"If Lorenzo Grove Chesterton or Ernest Herbert Chesterton, who were last heard of in August 1894, Los Angeles, Cal., will communicate with Messers A.F. and R.W Tweedie, 5, Lincoln's-in fields, London, Eng., they will hear of something to their advantage."
The Lincoln's Inn area is full of legal types.