I guess it depends on what part of "culture" you are looking at.
Tolkien actually invented Orcs and his image of Elves is what most people now see Elves
as looking like (being tall with pointy ears).
So Lord of the Rings vastly influenced video games and board games from Warcraft, to Warhammer, to Dungeon and Dragons,
to Everquest, to Morrowind/Skyrim, etc.
Basically anything in the "fantasy" genre of books, games or movies likely has copied things from Lord of the Rings.
Tbh, other than being highly popular, I don't see what Star Wars has brought to the table in terms of influencing the science fiction media other than
maybe light swords and use of special effects.
Btw, I was a Star Wars fan since I was a child and didn't even know Lotr existed till the first movie came out but facts are facts. I did however know about Orcs, Goblins, Elves etc before the first movie (not that they came from Lotr, but games I played had them in it).