I came across this ancestor to “LOL” in the most recent K9YA Telegraph (free subscription), taken from the Chicago Daily Tribune of November 17, 1938.
[The] Continental Morse code of amateur radio is the only language known to man with a specific expression denoting laughter or appreciation thereof. HI [.... ..] is understood as, “What I have just said is funny. Consider me as laughing, and join me if you wish.” In response it means, “I agree that your remarks are funny. Consider me as joining in your laughter.”