Luna Gakki were founded in Okayama in 1936 and through the 1940's, 50's and 60's were a major independent and separate Japanese manufacturer, probably the most popular in Japan, apparently doing enough local business to not be involved with the OEM manufacture that was being carried out in Japan at the time; though there was a company called Rhythm Band Inc. of Fort Worth Texas that imported them under the Luna branding to the US. 

Back in Japan the Okayama factory burned down in the second half of the 1960's, (I have read 1966?) but by this time they had expanded with offices in Tokyo and Yokohama as well, so they survived the fire, however this fire combined with the waning popularity of the Ukulele was the beginning of the end for Luna Gakki. Production of Luna Ukuleles was now carried out, I believe, by Mituba Gakki and at some point Luna Gakki stopped production altogether. Kiwaya took over the name, (presumably they brought it? but I don't know when?), and now produce a range of Soprano and Concert Ukuleles largely for the Japanese market using it. I'm not sure but I believe that all Luna Ukuleles, both the old Luna Gakki ones and the modern Kiwaya made ones, are laminate. 

Also it should be noted that in the 1960's Luna put "model by Kamaka" on the box for their Pineapple but this was a poor translation and they meant it was a copy of the Kamaka Pineapple idea, not that it was in any way meant to be a fake of an actual Kamaka).
This brand is nothing to do with Armadillo Enterprises Luna branded Ukuleles and other fretted Chordophones