Ironically enough, this turns out to be something that I once knew and had since forgotten; following from those reminders I found, by way of Tolkien Gateway, that the relevant information is included in Richard West's TOLKIEN CRITICISM: AN ANNOTATED CHECKLIST , one of the very first Tolkien books I ever read** and for years my bible for tracking down other stuff (pieces by and about Tolkien). Under entry B109, page 34, RW gives Tolkien's reply to a query regarding whether he'd been influenced by Burroughs in his own writing:
"Source hunting is a great entertainment but I do not
myself think it is particularly useful. I did read many
of Edgar Rice Burroughs' earlier works, but I developed
a distaste for his Tarzan even greater than my distaste
for spiders. Spiders I had met long before Burroughs
began to write, and I do not think he is in any way
responsible for Shelob. At any rate I retain no memory
of the Siths or the Apt."
I haven't read Lupoff's book,*** but Doug points out that the Siths and Apt appear in the third of the John Carter books, which I also have not read (PRINCESS OF MARS being the only one I've read of that series).
So the evidence seems to be that Tolkien read a good deal of Burroughs' works but that like many readers gave up on the various series as they became increasingly formulaic. He definitely read a number of the Tarzan books and some of the Pellucidar books; there doesn't seem to be enough evidence to say whether he read any of the Mars books -- he might have read some and just happened to miss that one volume or he might have given them a pass altogether.
From what I have read of Burroughs' work, I have to agree with Tolkien that I don't see any influence on the Middle-earth stories, but admittedly there's a lot of Burroughs I haven't read so I may be missing something. Still it's nice to be able to confirm another bit of Tolkien's reading and his awareness of his contemporaries.
*thanks to Doug for pointing this out, and to both Doug and Charles for providing me with the quote.
**this is back in the day when there were only five books out about JRRT: Isaacs & Zimbardo, Ready, Carter, West, and Kocher, with a sixth (Ryan) reported to be out there but which none of us had ever seen.
***though I have read Fenton's 1967 biography of ERB