I know very little about the Lucky Dia brand. It is found on derailleurs manufactured in Japan in the 1950s and possibly early 1960s. I believe the brand may have belonged to a company called 'Katsumoto' - about which I also know nothing.

The word 'Dia' forms part of the name of the Dia-Compe brand, but I don't know if Dia-Compe and Lucky Dia are related.

You can see some images of Lucky Dia derailleurs in the famous May 1981 edition of New Cycling magazine. They are on page 132, page 133 and page 134.