Yes, I do know Dave Lewis and have seen some of his reproductions. I'm not sure if he's replicated the later black rexine covered cases such as you describe, so yours could well be original and worth as much as an original Webley canvas and leather case.
The plastic case I've shown with the Tempest was not of the same construction as the earlier cases, which, I suspect, is why not that many were sold.
The one I've pictured is now in someone else's collection, but I still have one with a Nemesis in it which I will photograph in due course, and still have an original black lid Tempest box complete with pistol and outer sleeve. I've also still got a Tempest in the later brown cardboard box.