Heinz Edelmann (1934-2009) is most famous for his distinctive design and art direction on the Beatles-inspired Yellow Submarine (1968), but his Lord of the Rings covers—for the first German edition, translated by Margaret Carroux with help from Ebba-Margareta von Freymann—are a very close second. (Unfortunately, I could only find a larger scan of the Fellowship of the Rings cover.) There was nearly a Lord of the Rings movie starring the Beatles, if you remember.
A German paperback edition of The Lord of the Rings was also published by Klett-Cotta featuring new, equally mesmerizing cover art by Edelmann, as seen below, but I’m not sure about the year: Amazon Germany has it at 1977. The books came in a slipcase featuring additional art. You can see more of the case here. Note the shifting position and condition of the ring—is that the Eye of Sauron inside?—in this edition, .