Of American-English origin, free lunch, first recorded in 1842, denotes a lunch provided free of charge in a bar, saloon, etc., as a means of attracting customers.

For example, on Thursday 29^th 1847, the Morning Courier (Louisville, Kentucky) published this announcement:

Messrs. O’Mara & Gordon open their “Washington Exchange,” formerly the Washington Hall, to-day, with a free lunch. See their advertisement.

The advertisement in question was as follows:

The Public are invited to the opening of the Washington Exchange, to-day, at 10 o’clock, A.M., at which time a sumptuous Lunch will be served for the accommodation of visitors. Come one, come all.
Washington Exchange.—The undersigned respectfully inform the public that they have leased and fitted up the large and spacious house on Fifth street, known as the Washington Hall—for the purpose of keeping a Tavern.
All persons who may patronize this establishment, may rely upon good accommodations, prompt attention, and excellent fare, as the Proprietors will spare neither pains nor expense to gratify.
                                                                                                                          O’Mara & Gordon.

The phrase there is, or ain’t, no such thing as a free lunch means that everything inevitably involves a cost of some kind.

In an interview published in The Sterling Standard (Sterling, Illinois) of Thursday 23^rd December 1897, the diplomat used there is no such thing as a free lunch in its literal sense:

Nothing Free in Europe.

Edward L. Pricket of Edwardsville, Ills., late United States consul to Kehl, Germany, was here recently on his way home. He spoke freely and in an interesting manner of his experiences abroad. He said: “There is no such thing as a free lunch in all Europe. In fact nothing is free there. Even in Germany you have to pay for your pretzels, and they do not even give a match gratuitously. I went to Europe a free trader. I return a protectionist. I would like to see a tariff high enough to shut out all foreign manufactures. There ought to be some penalty put upon our rich people who go to Europe and spend their millions. But for American patronage half of the hotels in Germany, France and Switzerland would close their doors. Every hotel man, inn-keeper and petty tradesman gouges people from this country. They look upon all Americans as rich fools; and show no respect to our people in any way whatever.”

The following paragraph from the Ashland Weekly News (Ashland, Wisconsin) of Wednesday 30^th May 1888 indicates why Edward L. Pricket complained that “in Germany you have to pay for your pretzels”:

“Here’s one good thing,” yelled a free lunch fiend last night as he sprang at a dish of tempting looking eatables in one of the palatial new sample rooms just opened a few days ago. “This is something that ought to have been started several years ago in this town,” continued the fellow between gasps, as he masticated the tempting food and crammed his pockets full of the lighter stuff. “These old fashioned [sic] folks in this town don’t know what a good free lunch is—to folks who can’t board at a hotel. The only thing that I ever struck in Asland [sic] that looked or smelled like a free lunch is some old pretzels or some stale crackers and Limburger cheese. This is a godsend,” and the bum smacked his lips as he downed some other delicacy.

The earliest instance of the phrase used in its current sense that I have found is from the following letter, published in The Indianapolis News (Indianapolis, Indiana) of Wednesday 18^th January 1939:

Free Lunch
To the Editor of The News:
When Bruce Barton made the keynote speech at the Indiana Republican state convention last summer he said something that the New Dealers* can not [sic] seem to get through their heads—“There is no such thing as a free lunch.”
PAY UP.
Indianapolis.

* The New Deal was the programme of social and economic reform planned by the administration of Franklin D. Roosevelt from 1932 onwards to counteract the effects of the Great Depression; it involved a massive programme of public works and the large-scale granting of loans. Franklin Delano Roosevelt (1882-1945), American Democratic statesman, was the 32^nd president of the USA from 1933 to 1945.