First, don’t assume your audience is ignorant just because you only recently learned something. 🙂
Middle-earth should be written with a hyphen but no capitalization of the e in earth (because this is how Tolkien himself wrote it).
Add a comma after Middle-earth.
Change alongside to with (because alongside is awkward and doesn’t mean quite the same thing as with anyway).
I don’t know what the writer of the list was thinking, but achieved is very much the wrong verb for that sentence. I changed achieved to saw to it. I also replaced in order to with so he could.
Add the before company.
After Aragorn died, Legolas headed to the Grey Havens to leave Middle-earth, taking Gimli with him. Galadriel saw to it that the Dwarf was admitted into the Undying Lands so he could spend the rest of his days in the company of his best friend.
Kudos to the person who made that list, though, for spelling Grey correctly.
(I bet you’re curious about what WordPress’ spelling checker made of the proper nouns in this post… It wants me to change Legolas to Lego’s and Galadriel to Gamaliel. *shakes head*)