The Essence of the Tale

[Tar-Jêx]

I think that to be Lord of the Rings, it must follow the general storyline.

Hobbit gets a ring.
Hobbit must take ring to Mordor.
Hobbit faces many challenges, and must make sacrifices to finish the quest.
Hobbit goes through mentally scarring events.
Ring is destroyed.
Insert any important plot details relating to these points, like the Battle of the Pelennor Fields, Helm's Deep, the trip through Moria, Gandalf falling (very important).
Insert wacky and family friendly villains, like Bill Ferny, a few hundred thousand orcs, scary old men with magic voices, demons, and a huge, nightmare inducing, eye.

I will judge how accurate it is to the source material, but as long as it is relatively close, and comparable to the original source, it can be Lord of the Rings.