I hear that a new order of Knighthood is on the tapis—O.M.G. (Oh! My God!)—Shower it on the Admiralty!
The letter was in his Memories, published in 1919.
The OED has used this as historical context for adding OMG to their latest addition, along with other internet speak that I can't be bothered with recalling at the moment. Probably something like "fIRSt!!!111one1!!!1"