Bertram Lynch is an agent with the P.C.B.
That acronym stands for the Permanent Central Board, a part of the League of Nations. Looking up the history of this organization, it got its origin in 1925, eight years before the activities of Lynch in the first recorded adventure. It was originally the International Opium Commission and later the Permanent Central Narcotics Board when its purview was expanded.
Whether Lynch is a full-time employee of that organization or actually a British Intelligence operative working temporarily for the P.C.B. would be a valid question since we see Lynch involved in more than just anti-opium operations. Another valid question is just how long Lynch would continue working for that group before going back to what was his obvious first employers (i.e., British Intelligence). He was definitely on P.C.B. business on the first assignment we have but honestly states at the beginning of the second that he was involved in "special work" not really P.C.B. related. In the two remaining tales, taking place many years later, the League of Nations no longer existed so neither did the P.C.B. but his authority, especially in British Colonies, remained impressive.
What is not the least bit in question, though, is the fact that Lynch operates with considerable authority wherever he goes and he does so in the most serene manner. This fits beautifully the manner of man that we are told Lynch is by a man who would meet Lynch on that initial adventure, Professor Deane, and who would be asked to help out in each of the remaining three 'missions'.
According to Deane, Lynch as simply "the most ordinary man on board [the ship where they first met]". To Deane's opinion, he was "too ordinary". He was "of medium height, average weight, and middle age. His voice is flat and expressionless, and his accent puts him down as middle class". Despite the heat in the tropical area of that adventure, "he wore a gray suit and a gray felt hat". More curious to Deane was that "during ten days of increasing intimacy I had continuously hinted that I was curious to know what he did. I had learned nothing". Further, Deane opined his new friend was "too typical, too un-special. His ordinariness had a hint in it somewhere of overemphasis. As if that obscurity of his was a performance - a deliberate imposture".
[Note: in an April 3, 2009 Mystery*File review of the Lynch mysteries by David L. Vineyard, Mr. Vineyard recounted a simple event early on in the first adventure dealing with a hat, one that I also found very telling. Standing along the rail of the ship they were on, Deane observed how a gust of sudden wind swept the hat from Lynch's head. "His left hand rose, retrieved the vagrant felt from mid-air, and returned it accurately to its place. One smooth, single gesture and that was all". Deane goes on to say that except for that fluid, low-keyed grab, "not a single muscle of Lynch's body or face had stirred". Deane opined "never before had I seen such absolute self-possession, such faultlessly controlled response to an emergency".]
Lynch's calmness and his control has an interesting side-effect, at least as his new protegee is concerned, in my opinion. Lynch obviously likes Deane and comes to consider him a friend. He also puts Deane into quite deadly situations with little or no compunction. Giving him the benefit of the doubt, it is likely that Lynch would not have fretted about getting out of the danger himself so perhaps he just assumed Deane would as well.