The publication of The Lord of the Rings, and in particular the explosion of its popularity after 1965, did not result in an overnight transformation in the way fantasy was perceived and written. Indeed, the dominant form of fantasy throughout the 1950s, 1960s and 1970s remained sword and sorcery of the kind pioneered by Robert E. Howard.
Sword and sorcery and epic fantasy are distinct subgenres, although sharing some similarities (and both can be jointly referred to as secondary world fantasy). Sword and sorcery is seen as primarily action-driven, with violence and magic being dominant forces. Sword and sorcery books are generally shorter, and although often arranged in series there are perhaps less links between each book, with the focus more on stand-alone adventures. In the middle of the century sword and sorcery could also be quite weird, taking on board influences from science fiction as well as the fantastic.
Sword and sorcery had become the dominant form of fantastic fiction thanks to the likes of Howard and Leiber, and the work of other authors like L. Sprague de Camp and Lin Carter in popularising and expanding the genre. However, and perhaps surprisingly, it was this seemingly masculine subset of fantasy that brought in the first major female writers to the genre.
Starting in the 1930s, C.L. Moore wrote a number of short stories in both the science fiction and fantasy settings. Her works appeared in magazines such as Weird Tales and Astounding. Moore is notable for introducing one of fantasy's first heroines in the Jirel of Joiry series. In the following decade Leigh Brackett began writing numerous sword and sorcery-like stories, but set these on other planets like Mars and Venus, hence having them categorised as planetary romances (the same fate also befell male authors, most notably Edgar Rice Burroughs's Mars-set Barsoom series which arguably has more in common with swords and sorcery then science fiction).
In 1963 Andre Norton published Witch World, in which a man from our world is transported to a fantasy realm of warring factions. It is later revealed that people from other worlds and universes have been brought to this planet and the fantasy-like backdrop is melded with science fiction ideas. Norton wrote or co-wrote more than two dozen novels, novellas and short stories in this setting, and allowed other writers to use it as well. Witch World introduces the idea of having a fantasy world where only women can use magic, an idea later utilised by Robert Jordan in The Wheel of Time (unlike that series, men can also use magic safely and later learn to do so).
Male writers also continued to expand the remit of sword and sorcery and take it in unusual directions. In 1961, Michael Moorcock published The Dreaming City, which introduced readers to the character Elric of Melnibone. An albino riven by angst and introspection, Elric was deliberately designed as the antithesis of traditional heroes like Conan. The early Elric stories ended with the annihilation of Elric and his world; later books and novellas would fill in his backstory. Moorcock, who swiftly gained a reputation as the enfant terrible of science fiction for his introduction of the New Wave of the genre, enjoyed skewering holes in the perception of fantasy as well. In the 1970s he published controversial criticism of Tolkien (for his conservatism) and H.P. Lovecraft (for his racist viewpoints that spilled over into some of his fiction).
Rewinding a little to the same year that The Lord of the Rings was published, 1954, Poul Anderson released his seminal fantasy The Broken Sword, a gritty story of war, death and magic based on Viking mythology. Although relatively obscure today, writers from Moorcock to Richard Morgan have sung its praises as a demonstration of a darker, less comfortable form of fantasy to that written by Tolkien. Indeed, some have cited The Broken Sword as the forerunner of the so-called "grimdark" movement of fantasy that would eventually continue through Stephen Donaldson to more contemporary authors like Scott Bakker and Mark Lawrence.
In 1968 another author took a step into the ring to write a work that was neither Tolkienesque, nor sword and sorcery. Ursula K. LeGuin's novel A Wizard of Earthsea was set in a (mapped) fictional archipelago with a predominantly black cast of characters, a fact lost on the writers of the poor SyFy mini-series based on the books. The book inverted the fantasy stereotype of wizards being wise old men by asking where they came from and how they learned to do magic. This began the "magical academy" trope of fantasy fiction, which later found its ultimate form of popularity in the Harry Potter series (and echoes may also be detected in Susanna Clarke's Jonathan Strange and Mr. Norrell). A Wizard of Earthsea and its sequels are probably the closest we have to a "traditional" epic fantasy series between Tolkien and 1977, the year in which the modern genre really came into being.
In the same year, Anne McCaffrey published Dragonflight, the first novel in the Dragonriders of Pern series. Dragonflight is many respects an epic fantasy, but also a "rationalised fantasy", where the fantastic elements are explained by a science fictional background. The Pern series, despite its nominal SF background, would go on to influence many future fantasy novels, particularly with its depiction of dragons as allies and mounts rather than simple monsters.
Other authors continued to write tales of the fantastic without following up on Tolkien's lead. In 1970 Roger Zelazny published Nine Princes in Amber, about a man who discovers he was really destined to rule Amber, the one true world of which all others are reflections. This was the first of The Chronicles of Amber, which eventually extended to ten novels and enormous critical acclaim. Patricia A. McKillip achieved a significant breakthrough with her third novel, The Forgotten Beasts of Eld in 1974, but then surpassed it in 1976 with The Riddle-Master of Hed, the first novel of The Riddle-Master Trilogy. Children's fantasy also became more popular around this time, with notable works of juvenile fantasy including the Dark is Rising sequence by Susan Cooper (1965-77), Bridge to Terabithia by Katherine Paterson (1977) and Elidor by Alan Garner (1965).
However, the biggest and most successful juvenile fantasy of this time was Watership Down by Richard Adams, published in 1972. At first glance this book about rabbits has little to do with epic fantasy, but some of the tropes of the genre can be found within its pages. There is the lengthy, dangerous quest through unknown and hostile territory. There is a complex mythology including creation myths and spirits representing death. There is even magic, in the form of seers and visions. Foreshadowing the YA novels of modern times, the book is also fairly grim for a children's story, with major characters dying. Unusually, the novel's darker and more violent aspects survived into the excellent 1978 animated film adaptation.
By the latter part of the 1970s fantasy was a thriving form of fiction, but no-one had stepped forwards to really follow up The Lord of the Rings, or do something different with that form of fantasy. There was one last piece of the puzzle to slot into place before that would start to happen, and it came from two Americans who were not authors of fiction. Instead they were nascent game designers by the name of Gary Gygax and David Arneson, and the impact their creation would have on modern fantasy would be second only to Tolkien.