Neither Narnia nor The Ring became quite the pheenom that HP did.
I’m assuming by “The Ring” you mean The Lord of the Rings. If you’re talking the books, of course not. Both Narnia and LOTR were published in a very different era, without the huge marketing machine that Harry Potter did. Although LOTR was, relative to other books, a huge phenom in the 60s and early 70s.\
If you’re talking about the movies, the LOTR movies did better box office than the first three Potter films. The Fellowship of the Ring did just about the same box office as HP and the Sorcerer’s Stone, about $315M US domestic and $900M worldwide. But box office for the second two LOTR movies rose, but it fell for the next two HP films, although the movies did extremely well by any objective measure. The movies were all released about the same time, the first two pairs for the holiday seasons of 2001 and 2002, with Return of the King in December 2003 and the third HP film for the following summer. So direct comparisons are actually quite meaningful.
The Lion the Witch and the Wardrobe did somewhat less than the first LOTR and HP films, but better than the subsequent HP films. The next two Narnia films weren’t in the same league, but still each grossed in the $400+M range worldwide.
[All box office figures from Box Office Mojo]