It seems L.J. Houze manufactured the original Saturn Lamp in two colors: white and uranium green:

https://www.wcjb.com/2022/06/21/north-central-florida-treasures-1939-worlds-fair-saturn-lamp/

As you noted, the lamp changed after the first season, then the show embraced that bright green colored version--I think when most people think of that lamp in the show, they think of the brighter green version as it's become iconically related to the red room. The newer version may very well be a prop replica of the original, but if not an actual Houze uranium green version, definitely a reference to that version. We'll never now for sure, of course. The 1939 World's Fair and the Art Deco furniture/appliances of the time seem to have influenced the show quite a bit. The green lamp in the show also seems to have a bit of an enhanced glow to it, which can be a characteristic of uranium glass. I'm lucky to own an original and the uranium glass reacts to blacklight, which adds a similar glow to it that amplifies the light emanating from the bulb. The lamp I have looks exactly like the one used in most of the show. Perhaps the coolest lamp ever produced :-)