Actually Lord of the Rings was done by Ralph Bakshi - a 
different studio all together. Rankin/Bass did the first
two installments of the trilogy, The Hobbit and 
Return of the King. 

The Bakshi work really doesnt resemble anime at all - 
the character design and quality of animation is much 
poorer, in my opinion. And I am fairly sure that the
production staff for the Bakshi film was not Japanese -
as was the case for the Rankin/Bass films. That is probably
why it is fairly easy to buy Lord of the Ring cels from 
western animation art galleries; whereas finding 
Rankin/Bass cels is generally much more difficult.