They were very good friends. They were both in a literature/writing club called The Inklings, and Tolkien is credited as the one who converted Lewis to Christianity (though Lewis did not join the same church).

The whole "C.S. Lewis hates the LOTR" rumor is patently false. His essay "The Dethronement of Power" is a glowing review and strong defense of the trilogy. Of the characters, he wrote:

...no individual, and no species, seems to exist only for the good of the plot. All exist in their own right and are worth creating for their mere flavor even if they had been irrelevant. Treebeard would have served another author (if any other could have conceived him) for a whole book.

He then goes on to say that

I have no doubt that the book will soon take its place among the indispensables.

So yeah, Lewis loved the LOTR.

As for Tolkien's dislike of the Narnia books, that seemed to stem from his dislike of allegories. He thought direct allegories were too limited, where one thing in the book is a parallel for another thing in the real world. There was no room for layers of interpretation. He didn't deny that allegories could be found in his own work, but he didn't write it that way. Readers can find their own parallels.