It's important to remember that Peter Jackson's Lord of the Rings trilogy was itself "lightning in the bottle." New Line took a huge gamble greenlighting the trilogy as a trilogy, and if Fellowship had failed... well, let's not think about that. The next two films would still have come out, but they'd probably have been butchered in the running times, the extensive Two Towers reshoots wouldn't have happened, etc.
There's a book titled The Frodo Franchise that takes a look at how Jackson hit at the right time -- the internet was close to mainstream, the DVD market was taking off and had lots of possibilities for expanded content that Jackson really took advantage of. And there was an intense marketing effort that got people -- like my sister, who I would have never thought would ever want to watch it -- in the theater to see it.
Will the television series be "lightning in a bottle"? I doubt it. I'm not saying it is going to fail, that's not what I mean. But Amazon's expectations for the series are... what? Drive sign-ups on Amazon Prime? (That's a mature market; there's not a lot of growth there.) Sell more books? (They'll get a cut as the seller.) Get a cut of the licensing based on the series?
I remain a little skeptical that a streaming series can truly achieve mainstream penetration in the way a movie or a broadcast (basic or premium) television series can due to barriers to entry (both monetary and technological) that cable television or a movie theater don't have.