I once read that Lord of the Rings was popular among hippie culture in States, how did this happen?

To a large degree it had to do with availability; The Hobbit and The Lord of the Rings were both published in hardcover in the United States in the 1950s, and there was an American fan scene for Tolkien's work by the early 1960s, part of the sprawling network of fanzines, clubs, and amateur press associations. Author Marion Zimmer Bradley famously published a fanfiction "The Jewel of Arwen" in the 'zine I Palantir #2 (August 1961) - but the introduction of Tolkien to a general audience occurred when The Lord of the Rings hit paperback.

The first paperback edition was actually a pirated edition by Ace published in 1965; this spurred Ballantine Books to issue an authorized paperback edition, which became a bestseller. You can read a few more of the details about this incident in MIDDLE AMERICA MEETS MIDDLE-EARTH: AMERICAN PUBLICATION AND DISCUSSION OF J. R. R. TOLKIEN’S LORD OF THE RINGS, 1954-1969, but the upshot was that hippies coming of age finally had ready access to the book in an affordable format - and the popularity of those paperback editions spun-off associated media like The Tolkien Reader (1966), Leonard Nimoy sang The Ballad of Bilbo Baggins on Two Sides of Leonard Nimoy in 1968, Smith of Wooten Major and Farmer Giles of Ham (1969), Lin Carter's Tolkien: A Look Behind the 'Lord of the Rings' (1969), the parody Bored of the Rings (1969), Robert Foster's A Guide to Middle Earth (1971), etc.

This was actually the spur for a larger trend of a resurgence in fantasy fiction in the United States; Carter served as the editor of the Ballantine Adult Fantasy series (1969-1974), which reprinted many classical works of fantasy in paperback editions - the "Adult" indicating that they were meant as serious literature, as opposed to kiddy fare, not implying any pornographic or obscene content. Authors included Lord Dunsany, E. R. Eddison, William Morris, H. P. Lovecraft, Mervyn Peake, and James Branch Cabell. Tolkien and these other fantaisists served as the direct inspiration for a huge amount of subsidiary fiction, from fanfiction to original fantasy novels and trilogies.

And why was Lord of the Rings popular among hippie culture?

In The Hobbit and the Hippie by Flinn and Ratcliffe argued that, aside from some cosmetic appeal (flashy covers, etc.):

we note that both Professor Tolkien and the hippies reject (1) the “rationalist progressive” view of history as a series of distinct improvements over the past and (2) the materialist belief that matter is the ultimate determinant of all things. In spite of the fact that Professor Tolkien and the hippies agree merely in the rejection, not the grounds for rejection, here is a kinship which might make a hippie feel at ease in the world of The Lord of the Rings.

But they also note that this explanation is inadequate; certainly not enough to explain the popularity for "Gandalf for President!" or "Frodo Lives!" The fact is that some works just resonate with certain crowds when presented at the right time; the tale of peace-loving, sedate hobbits and the evil empire of Mordor happened along at the time when the United States was engaged in a military draft for an unpopular war just...clicked. The reasons were probably as varied as the hippies themselves, and I don't want to delve into speculation on all of that.

Also, what other works of fiction was popular among hippies?

H. P. Lovecraft also hit a huge resurgence around the same time, and for more or less the same reasons: cheap paperback reprints, this time from Ballantine and authorized by Arkham House, who more or less controlled the rights at the time; as well as the publication of underground horror comix and comic magazines featuring Lovecraft's creations, which were sold in head shops; this was, bizarrely, accompanied by one of the first and most prominent film adaptations of Lovecraft's fiction, The Dunwich Horror (1970) - which featured some bizarre psychedelic scenes involving hippies! Lovecraft also had some considerable musical influence, most notably the American psychedelic band H. P. Lovecraft; their eponymous first album was released in 1967.