But I'm pretty certain the changes you're referring to, the substantial revision to the 'Riddles in the Dark' chapter of
The Hobbit to bring that story in line with what
The Lord of the Rings said happened, were executed in the second edition of
The Hobbit, which was issued in 1951.
The changes were based on a purported thought experiment by Tolkien as he came to the end of writing
LotR in the late 1940s: he sent his publisher a kind of "this is how it should have been - what do you think?" manuscript. But at the time no reprint of
The Hobbit was in the works. A few years later the second edition was issued, and Tolkien affected to be shocked and surprised to see his changes set in print!
I have an older reprint of that edition, from the early 1960s, and there is a funny note just before the story begins, where the author explains the changes from the first edition.
"In this reprint several minor inaccuracies, most of them noted by readers, have been corrected. .... More important is the matter of Chapter Five. There the true story of the ending of the Riddle Game, as it was eventually revealed (under pressure) by Bilbo to Gandalf, is now given according to the Red Book, in place of the version Bilbo set down in his diary. This departure from truth on the part of a most honest hobbit was a portent of great significance. It does not, however, concern the present story, and those who in this edition make their first acquaintance with hobbit-lore need not trouble about it. Its explanation lies in the history of the Ring, as it is set out in the chronicles of the Red Book of Westmarch, and it must await their publication."
In short, the change hit
The Hobbit before
The Lord of the Rings was published, and made no particular sense to fond and loyal readers of
The Hobbit at the time! And that major change to the first book was practically ancient history by 1960, when the even more major rewrite was aborted.
Getting back to the 1966 third edition, I myself cannot remember what the changes were, which is why I referred to them as minor, particularly in comparison to what Tolkien had hoped to do in 1960 about rewriting the book from start to finish to align it in style and tone with the trilogy.