Strictly speaking, I don't think this is what happens in LOTR. Yes, some of the books in LOTR run in parallel (as regards calendar time), but the stories in these sections are told in time-order (give or take the retelling of otherwise unseen events by one character to another).
As for my own WIPs, I did start with Book 2, although I didn't know it at the time. Like Wagner (who realised that Siegfrieds Tod - now Götterdamerung - needed something to help the opera-goer make sense of it, and so wrote, eventually, three prequels), I decided an introductory volume was required, even before I finished the original book**. That's sometimes how it is.
If a work is a trilogy (or whatever), a slicing up of one big story, tell it in the best order for the reader to understand (at the approriate time) what is going on. A series is different: you can add whatever you like. But as someone has already said, be careful about spoilers that ruin any intended suspense in a book that could be read later.
** - Needless to say, what is now Book 2 bears little ressemblance to that earliest version.
