The first book illustration anyone ever saw of Gollum came in the 1977 Harry N. Abrams, Inc., edition of The Hobbit.
This work was released in tandem with the Rankin/Bass animated movie version of The Hobbit, which aired on November 27, 1977, on NBC. Lester Abrams was hired to do the character designs based on his covers for Children's Digest in 1974. Because his original depiction of Gollum was considered too innocent, Arthur Rankin told him to come up with a much more menacing figure.
As far as I can tell, this was the first published (e.g., book) depiction of Gollum. None of The Lord of the Rings editions, either separate volumes or slipcase editions, contained anything other than maps until the 1980s. Nor did any of the editions of The Hobbit. This was not only the first Tolkien publication to contain non-Tolkien art, but it was the first of the two novels to depict Gollum -- as well as a number of other characters.
One can easily see what Abrams did to make Gollum more terrifying. The eyes are huge, with gigantic pupils. There are fangs, the more is far more lizard-like, there are claws, and the creature looks toadish and unhuman.