I don't do that with LoTR but I do with Alan Moore's Watchmen. I used to read it every summer. Skipped the last two so I am especially enjoying it this time.
I first read LOTR when I was 10/11, and I have not read it straight through in order since. I've re read certain parts many times, and probably read the whole content at least 3 times total. I've probably read "The Mirror of Galadriel" dozens of times.
However, I started it again from the begining in August. Although I realized after I probably should have waited for September.
Also, Wombat infected me with his "October Country" re-reading thing
For me, The Lord of the Rings gets better each time I read it. I discover more nuances in the writing, themes, and mythological "echoes" each time. That said, I envy those who have never read it . . . they get to read it for the first time!