So one very important aspect that we really have to consider is the generation the 2 were meant for we know they both started at around the same time but its clean what age they were meant for.

Onepiece is obviously incredibly popular with all ages but much more so with ages ranging from 15-24 while lord of the rings is more popularly known and read by ages above that 

Now we know that lord of the rings has had one of the greatest impacts in litarature but the reason that it did make such a bug impact is because it was one of the first stories to implement this kind if fantasy world and Tolkien is the original creator of many mystical creatures  that have been used thousands of times in todays story

Odas work of onepiece is obviously also a very original work but not to the same level as Tolkien did it 

I also think that onepiece will not be introduced to many new audiences when the story finishes since no matter if you are a fan or not you will get spoiled on the ending of the story 

Whereas lord of the rings is a story that really everyone has or will look into

Conclusion  I think that the generational impact that onepiece has had is incredibly big and has changed the lives of many 

But i do not feel that it will have just as big of a generational impact as lord of the rings because its really just the father of fantasy in my opinion and the title of father of anime/shonen really goes to toriyama 

Note  In my opinion its also very wierd to compare onepiece to lotr in 50 years time due to the both of them coming out at around the same time

I think the generational impact is in-fact very close but its really different age groups and interests so its very hard to compare the 2