In *The Memoirs of Herbert Hoover: The Cabinet and the Presidency 1920-1933,* pp. 221-2, Hoover wrote as follows concerning his choice of a Cabinet after his election in 1928:
"When I formed the Cabinet, I came under strong pressure to appoint John L. Lewis Secretary of Labor. He was the ablest man in the labor world. In view, however, of a disgraceful incident at Herndon, Illinois, which had been greatly used against him, it seemed impossible. He, however, maintained a friendly attitude. As he stated publicly in later years, 'I at times disagreed with the President but he always told me what he would or would not do.' Lewis is a complex character. He is a man of superior intelligence with the equivalent of a higher education, which he had won by reading of the widest range. He could repeat, literally, long passages from Shakespeare, Milton, and the Bible. His word was always good. He was blunt and even brutal in his methods of negotiation, and he assumed and asserted that employers were cut from the same cloth. His loyalty to his men was beyond question. He was not a socialist. He believed in 'free enterprise.' One of his favorite monologues had for its burden: 'I don't want government ownership of the mines or business; no labor leader can deal with bureaucracy and the government, and lick them. I want these economic royalists on the job; they are the only people who have learned the know-how; they work eighteen hours a day, seven days a week; my only quarrel with them is over our share in the productive pie.'
"If Lewis's great abilities could have been turned onto the side of the government, they would have produced a great public servant."
http://www.ecommcode.com/hoover/ebooks/pdf/FULL/B1V2_Full.pdf
(There is no "Herndon, Illinois"; obviously Hoover meant "Herrin, Illinois." See
http://en.wikipedia.org/wiki/Herrin_massacre and
https://web.archive.org/web/20050210082822/http://www.geocities.com/heartland/7847/massacre.htm for the details of the 1922 "Herrin massacre.")
Anyway, Hoover decided to re-appoint the Harding-Coolidge Secretary of Labor, James J. Davis.
http://en.wikipedia.org/wiki/James_J._Davis But in November 1930, a second opportunity arose to appoint Lewis. Davis was elected to the US Senate from Pennsylvania and Hoover had to choose a successor. According to Irving Bernstein, *The Lean Years: A History of the American Worker, 1920-1933*, p. 354,
"The American Federation of Labor had traditionally regarded the Department of Labor as its own and the Secretary of Labor as its voice in the Cabinet. Gompers had played the decisive role in the creation of the Department on March 4, 1913. No one from outside the AFL had ever been Secretary of Labor...Shortly after the Davis announcement, [William] Green [Gompers' successor as head of the AFL] called at the White House to ask the President to name a man from the Federation. He suggested five prominent leaders: William L. Hutcheson of the Carpenters, John L. Lewis of the Miners, Matthew Woll of the Photo-Engravers, John P. Frey of the Metal Trades, and John R. Alpine of the Plumbers. Green urged Hoover to 'maintain the precedent set by your predecessors.'
"The President, however, chose to break with tradition. He appointed William N. Doak of the independent Brotherhood of Railroad Trainmen as Secretary of Labor. In Hoover's judgment the AFL could be ignored even on an issue of moment."
The idea of Lewis as Hoover's Secretary of Labor intrigues me in part because the two men were philosophically compatible in many ways. I don't just mean Lewis' opposition to socialism and communism--that was commonplace among American trade unionists. What was more unusual is that Lewis shared the engineer Hoover's enthusiasm for technological advance and modernization. Notoriously, many labor leaders opposed the introduction of new technology for fear it would put people out of work. Lewis, however, wanted the coal industry to become more modern even if that meant employing fewer coal miners. Mechanization would help put out of business the smaller, less efficient mines that were driving down coal prices and wages. As Lewis put it, "We decided it is better to have a half million men working in the industry at good wages...than it is to have a million working in the industry in poverty." (Bernstein, p. 225) Moreover, Lewis endorsed Hoover for the presidency not only in 1928 but for re-election in 1932 as well (despite Hoover's having turned him down for Secretary of Labor twice). Lewis' politics later in the 1930's could hardly have pleased Hoover, but in 1940 they were allies again--Lewis even trying to get the Republicans to nominate Hoover for president on a stay-out-of-the-war platform.
I do not know to what extent the Herrin massacre was responsible for Hoover's decision not to appoint Lewis, but let us assume that Hoover was telling the truth in giving this as his reason. Our POD can be that the massacre doesn't occur. (We'll say W. J. Lester decides not to resort to strikebreakers.)
There is probably not much Lewis could do for labor as Secretary under Hoover in the conditions of 1929-33. But his taking the post could have important consequences anyway. Even before the Depression, the coal industry and the UMW were in a bad way in the late 1920's, thanks to the opening of new, low-wage coal mines in the South and increased competition from other fuels. The Great Depression, of course, made things infinitely worse. "The output of bituminous fell from 535 million tons in 1929 to 468 in 1930, 382 in 1931, and 310 million in 1932." (Bernstein, p. 360.) In OTL the bad condition of the coal industry helped to spark a series of challenges to Lewis from districts jealous of their autonomy. In Illinois, this led to a rival "reorganized" anti-Lewis UMW which for a time dominated the coal fields of the state and later to the Progressive Miners of America. Lewis did ultimately manage to defeat the dissidents and retain control of a united though diminished UMW in OTL. But with him in the Cabinet and unable to take a direct role in UMW internal affairs, the union might have disintegrated altogether--there might not have been much for him to return to in 1933. Besides, having served as Secretary of Labor for the president most hated by the American working class would not help his future as a labor leader. With Lewis in a diminshed role, does the CIO ever get off the ground?