The first to discover lucid dreams was Dr. Keith Hearne in England.
I’m not quite sure where you got that information, but no, he wasn’t the first.
The practice of lucid dreaming is ancient. Sometime in the 5th century, a letter was written by St Augustine (I think) that mentioned Lucid Dreaming, which may have been the first written account of LD’s, though he practice predates it. The first scientific focused book on LD’ing was written in 1968, though many other books were written on the subject before 1968.
The term itself was coined in 1913 in a book by a Dutch psychiatrist, though it wasn’t very readily accepted by the scientific community.
I will say though, as far as I can tell Dr. Hearne may have been the first to create a scientifically accepted proof of Lucidity, in the 1980’s. (Using eye movements of dreamers)
So there you have it, a brief history of LD’ing. 
And also 
to LD4all 
And for some reason, Hearne was hesitant to publish his results. I think he wanted to gather more data or something like that before he brought his results forward. Indeed Stephen LaBerge did almost exactly the same set of experiments and published his results in scientific journals before he even heard of Hearne’s work 
Frederik van Eeden didn’t coin the term “lucid dreams” in a book, but in a presentation he held for an audience for the Society for Psychical Research in London. He classified several sorts of dreams, and lucid dreams were just one of his “categories” of dreams. The actual presentation can be found here: ld4all.com/what_lucid_paper.html
I’m a van Eeden fan 