Lewis himself was from the midwest, but he identified himself with the "Progressive" political movement in American politics - something that began very early in the century (or before). Such things become conflated and entangled in the real world.
Your second sentence says a mouthful. Despite the current contention (mostly among academics), the "progressive" movement began among Republicans in the late 19th century, and not as is the contemporary claim, among Democrats and socialists in the early 20th century. Theodore Roosevelt, Jr. and Henry Cabot Lodge were both Republican progressives in the 1870s and 1880s. When Roosevelt ran independently against Taft and Wilson in 1912, he named his party the Progressive Party. He is said to have written: ""To destroy this invisible Government, to dissolve the unholy alliance between corrupt business and corrupt politics is the first task of the statesmanship of the day."
--as a part of the Progressive Party platform, and he makes that claim himself in his autobiography.
Roosevelt entered the state assembly in New York in 1881, dropping out of Columbia Law School to do so (he had graduated Harvard in the previous year). He wrote and submitted more legislation than any other Republican assemblyman during his tenure, and almost all of his bills were focused on attempting to end what he thought of as the alliance between corrupt businessmen and corrupt politicians. His first fight was over elevated railway fares in New York, and he didn't start small, he took on Tammany Hall and Jay Gould.
Both Roosevelt and Lodge could not in good conscience support James G. Blaine in 1884. In those days, candidates for the office of President did not personally campaign, and both Lodge and Roosevelt were already well know as tireless campaigners, and appreciated for it despite the annoyance they caused with their "progressive" ideas. They were considered radicals by the establishment Republicans, the party bosses. Their refusal to campaign for Blaine (he was probably no more corrupt than most senators of the day, when most of them were still appointed rather than elected at large, but he was considerably more ham-handed and indiscrete; truth be told, if Lodge and Roosevelt knew about it, just about everybody did--they were not privy to the secrets of the inner circles of power in the Republican Party) was considered an unforgivable betrayal. Roosevelt's unpopularity with the Republican bosses continued right up to 1900, when the party boss in New York, who absolutely writhed with frustration at seeing Roosevelt in the Governor's mansion, engineered a tour de force
end run on Mark Hanna (McKinley's political handler and biggest contributor), and got Roosevelt put on the ticket as McKinley's Vice Presidential candidate. Talk about kicking yourself.
William Howard Taft was considered by Lodge and Roosevelt to be a progressive, too. Lodge was the "elder statesman" of the powerful duo, being older than Roosevelt, and having been appointed to the Senate in 1893. Ironically, Lodge had no such problems with the Party establishment, because he was a staunch supporter of conservative planks in the Party's platforms--but he and Roosevelt saw eye to eye on the necessity of ending political corruption and the influence of capital in the Party, and they both were ideologically opposed to "trusts" and devoted to the notion that the party of Lincoln must support the common man. Roosevelt, however, felt that Taft had betrayed their progressive principles once he got in the White House, and felt especially betrayed since he felt that Taft could not have been elected without his support--a claim subject to reasonable debate. That was why Roosevelt founded the Progressive Party and ran against Taft in 1912. If Roosevelt had not been the target of an assassination attempt, he might have defeated both opponents--or so some historical observers believe, although i'm not certain that i agree with that. In the event, the effect was to draw off enough Republican voters, but not so many Democrats (staunch Democrats never forgave him for his attacks on William Jennings Bryan as a party campaigner in 1896). Roosevelt's bid for the White House effectively handed it to Wilson.
It is perhaps attributable to that coterie of "intellectuals" of whom you have written that the idea that "progressive" means liberal. The original "progressives" on the American political scene were young "radical" Republicans like Roosevelt (and Lodge, although always saw himself as a conservative), who saw it as their mission to rescue the working class from both capitalist greed, and therefore from the Democrats and dangerous socialists like Bryan. Exactly the same thing, in a more cynical vein, can be seen in Canadian politics. In 1944, Tommy Douglas lead the CCF (the Cooperative Commonwealth Federation) to electoral victory in Saskatchewan, and scared the bejesus out of the Tories--it was the first true socialist government in North America. The Tories eventually succeeded in killing the CCF by branding them as commies, and successfully associating them in the public mind of Canada as fellow travellers with the Bolsheviks. But Douglas didn't just win one for the CCF, he lead his party to five successive victories, and ran Saskatchewan until 1960, and that in teeth of the howls of indignation when he brought in the first medicare program, and doctors in Saskatchewan went on strike (and caved in).
Alarmed, the Tories and Liberals ran to catch up, and even more than the Liberals, the Tories coopted populist sentiment by passing social legislation--in many provinces they even held their noses and voted for medicare (which in Canada means socialized medicine). The smear campaign against the CCF eventually succeeded, but out of the wreckage of the CCF, Tommy Douglas helped others to rebuild true left wing politics in Canada, and the New Democrats were created. The NDP has formed many provincial governments, including in Ontario on one occassion.
The Tories had been sufficiently spooked that they made "progressive" their watch word, and even the official name of their party. Until the national party imploded and accepted an alliance with Stephen Harper, they were known as the Progressive Conservative Party--the PCs (ironic initials, no?). The national party has a new name, but the Tories in Ontario still call themselves the Progressive Conservatives.
I would venture to say that the question of who gets to be a progressive depends upon whose ox you are attempting to protect from being gored.