That is going to be hard to find, but you could also buy a junker on ebay and get a base that has the bottom black plastic piece you need. Sometimes people just list a base for sale and not the entire lamp.
Thanks for the heads up,
Maybe someone is kind enough to replicate one from resin or acrylic just to name two of aproximately a million choices how to do this...and no I'm not in pesession of the piece in question but if you have missing pieces of some mathmos lamps I might stop being a dick for a brief period of time and magically become somewhat of a replicator untill its finished...just to become a dick again and rip you off on postage of course :)
FYI, this is an extremely early Century, probably the first design after the none-known-to-exist first model. I wouldn't even refill it.
I appreciate the recommendation. I don't know a lot about lava lamps, but I do mess with vintage furniture and lighting. The lamp's apparent age was the thing that caught my attention. It "felt" late fifties/early sixties just based on finish and construction. Clearly, after doing a little research, I realized they weren't made until a little later.
2 listing on ebay right now for century bases. Check it out.
As a guy that bought way too many vintage lamps thinking I would just clean and refill them I am in agreement with the response above from Jonas.
By the time you clean, goo kit, etc you would be better off just grabbing something that works from Ebay. Especially if this is new territory for you. Based on your carpentry skills I am certain you could get the base in nice working order but you may run into problems with a bottle that shows a thousand defects when it's lit, or a bad coil... not to mention tuning the fluids to flow correctly. JMO - trying to save you immanent frustration.