What were the changes made to "The Hobbit" after
"The Lord of the Rings" was written, and what motivated them?
[This question refers to the major revisions made to the Gollum chapter, "Riddles in the Dark", not to the multitude of minor changes made elsewhere.]
In the original 1937 edition of "The Hobbit" Gollum was genuinely willing to bet his ring on the riddle game, the deal being that Bilbo would receive a "present" if he won. Gollum in fact was dismayed when he couldn't keep his promise because the ring was missing. He showed Bilbo the way out as an alternative, and they parted courteously.
As the writing of LotR progressed the nature of the Ring changed. No longer a "convenient magical device", it had become an irresistible power object, and Gollum's behaviour now seemed inexplicable, indeed, impossible. In the rough drafts of the "Shadow of the Past" chapter Gandalf was made to perform much squirming in an attempt to make it appear credible, not wholly successfully.
Tolkien resolved the difficulty by re-writing the chapter into its present form, in which Gollum had no intention whatsoever of giving up the Ring but rather would show Bilbo the way out if he lost. Also, Gollum was made far more wretched, as befitted one enslaved and tormented by the Ruling Ring. At the same time, however, Bilbo's claim to the Ring was seriously undercut.
There are two issues involved, well summarised in the Prologue: "The Authorities, it is true, differ whether this last question was a mere 'question' and not a 'riddle' ... but all agree that, after accepting it and trying to guess the answer, Gollum was bound by his promise" (FR, 21). Thus, it was Bilbo's winning of the game that was questionable. Given that he had in fact won, albeit on a technicality, he was fully entitled to the prize, which, in the old version, was the ring. In the new version, however, he had no claim to the Ring at all, whether he had won or not, because the Ring was not the stake of the game.]
The textual situation thus reached was that there now existed two versions of the episode. Tolkien deftly made this circumstance part of the story by suggesting that the first time around Bilbo was lying (under the influence of the Ring) to strengthen his claim. (Bilbo had written this version in his diary, which was "translated" by Tolkien and published as "The Hobbit"; hence the error in the early editions, later "corrected".) This new sequence of events inside the story is laid out clearly in "Of the Finding of the Ring" (Prologue) and is taken for granted thereafter for the rest of the story (e.g. in "The Shadow of the Past" and at the Council of Elrond).
"The Hobbit" as now presented fits the new scenario remarkably well, even though Tolkien, for quite sound literary reasons, left this entire matter of Bilbo's dishonesty out (it was an entirely irrelevant complication which would have thrown everything out of balance). The present attempt to step back and view the entire picture is made more involved by the fact that there were two separate pieces of dishonesty perpetrated by Bilbo.
The first, made explicit, was that when he initially told his story to Gandalf and the Dwarves he left the ring out entirely -- this no doubt was what inspired Gandalf to give Bilbo the "queer look from under his bushy eyebrows" (H, 99). Later, (after the spider episode) he revealed that he had the Ring, and it must have been at this point that he invented the rigmarole about "winning a present" (an incredible action, given the circumstances). There is, however, no hint in the text of this second piece of dishonesty (as noted above, it would have been a grave literary mistake).
Readers are therefore given no indication that when "Balin ... insisted on having the Gollum story... told all over again, with the ring in its proper place" (H, 163) that Bilbo didn't respond with the "true" story, exactly as described in Ch V. In this regard, "Of the Finding of the Ring" in the Prologue is a necessary prelude to LotR.