How was Tolkien zero to hero? Bilbo was the only zero. Gandalf certainly wasn’t, and all of the dwarves were very well established warriors by the time they entered the story. Heck, Thorin was a freaking king. And in LtR, again the hobbits were the only zeros. Everyone else was already an accomplished hero in their own lands.
Also, the Grey Mouser and Fafhrd, while not weaklings, were not heroes when they were introduced. Fafhrd in particular has some issues that weren’t so heroic at first.
But, that's the point. It's called "The Hobbit" for a reason. It's not called "The Dwarves and a Hobbit".

Both The Hobbit and LotR focus most of the story on the Hobbits. They are central to the narrative. In LotR, Legolas and Gimli were mostly NPC's. And Gandalf was the DMPC.
But, the point being, that arc of zero to hero is largely missing from fantasy stories from before LotR. The Leiber stories are pretty late in the line to be honest, appearing some time after the Hobbit and LotR, so, we cannot discount the impact Tolkien had on Leiber's writing. I don't know what impact it had, but, it's entirely possible that it had some.
I think people tend to forget just how tiny Fantasy as a genre was prior to about 1980. Even by the 60's and 70's, there were only about a couple of dozen new Speculative Fiction (and that includes SF) novels per year. You could easily read all the new Spec Fic novels printed every year. To put it in perspective, there are now thousands of original Spec Fic novels published every year and that doesn't count media tie-ins like Star Trek or Star Wars novels. You couldn't possibly read more than a fraction of what comes out in a given year any more.
Did pulps have an impact on D&D? Of course they did. Did mythological stories have an impact? Of course they did. How could they not considering that outside of Tolkien that's pretty much all there was in the genre at the time? It's very interesting to note that when you look at Appendix N in the 1e DMG, virtually ALL the writers on the list had published within 10-15 years of the 1e DMG coming out. Again, of course they did because prior to that, you had hardly any published fantasy works to look at.
Trying to say that Tolkien had little or no impact on D&D is like saying Shakespeare has no impact on English dramatic stories.