Bollocks. You can play about the first three notes of Star Wars and people will recognize it. The same cannot be said of LotR. The opening crawl had been lampooned and parodied but still is always recognizable as referring to Star Wars.

There's no May the Fourth or Revenge of the Sixth two days later for LotR. Star Wars is a far deeper cultural touchstone that LotR. It is far more pervasive.

Beyond that, the Original Trilogy had spawned a prequel trilogy and a sequel trilogy, and no matter how shitty those are, they dwarf LotR. Add to that the myriad television shows, countless video games, endless references in other pop culture, and you run into the inescapable fact the LotR doesn't hold a candle to Star Wars.