I still believe the one on the Lee-Speed to be a modified Parker-Hale #16 like my "Ersatz Sportargets". Here is a photo of another one , this time on a M-S M1900, taken from about the same angle like the Lee. It merely has a slightly different, later elevation collar.

The one shown above by jc5 is again a Lyman #1 on a special base by Jeffery like shown in their pre-WW1 catalog, and the one offered by Prechtl is the Rigby copy I mentioned in my thread on "Classic Firearms" forum.