To use your lava lamp in another country there are some factors you need to understand.
Does it use the same plug?
Odds are it won't use the same plug.
Does it use the same bulb socket?
It might.E26 and E27 and GU10 sockets are interchangeable. Others are not.
Does it run at the same voltage?
This is probably the biggest hurdle. Most of the world either runs on 120v or 240v. In the USA 120v is used so if you take a light bulb meant to run in the UK at 240v even if you manage to plug it in it will run at half voltage and put out half of the heat so your lamp will not run.
So what to do? Well there are a few options listed in detail below.
UK to USA
No modding method
If you do not want to change the wiring buy a 120v to 240v step-up converter here.
You can either cut off the old UK style plug and replace it with a US blade plug. Polarity is not an issue with light bulbs so this is as simple as stripping the wires and screwing them in.
Cooper Wiring 183BKBX Non-Grounding Rubber Straight Blade Plug
Or you can use an adapter.
E14 is closest to the US E17 intermediate socket. Bulbs for these two sockets are incompatible. The socket will either need to be replaced or a step up converter will need to be sued. Same for the B15 socket.
E26 and E27 are compatible. They are only different by about 1MM. You can reuse the socket.
Newer Mathmos lamps use GU10 halogen bulbs. These are the best because they are available in the US in 120v versions and the socket is the same. Make sure to get a narrow cone version. The narrow ones concentrate the heat better and result in better flow. The wider cones do work, but not as well. They work without any modification.
If you want to run the Mathmos globes in Lava Lite bases it is recommended to use these bulbs in them as well if you are using a century base. They will need an E27 to GU10 adapter and the bulbs have to be the narrow cone ones because they are shorter. When used in this adapter they are about the same height as a typical appliance bulb.
Aristocrat bases work without any modification because they do not lose as much heat as century bases.
Astro globe on new Astro base: GU10 35W
Astro globe on Century base: R16 40W without the heat ring.
Astro globe on Aristocrat base: A15 40W.
Astrobaby: E17 25W reflector or E17 30W reflector depending on year.
Fluidium: E17 40W reflector. Use glass heat shield or the base will crack.
Jet: E17 25W reflector
Not sure if the formula is different in these, but they run great on E17 25W bulbs.
3/8th Threaded rods with waster and nuts. These are usually sold in kits. Having various sizes allows you to get a proper height on the socket.
Intermediate or E17 Base Porcelain Socket depending on bulb used
Ideally you want one with the threaded rod adapter already installed. This makes the work much easier.
This is in case you need to do any modifications to the length of the rod or the width of the washers. You may not need it.
Just replace the plug and use a 120v GU10 35W.
The bottom of the fluidium has a removable socket holder. Simply remove this and take out the old socket. Using your kit assemble the socket and run the cord through the rod. You may need to use some glue to hold it in place. Note with the kit used on this one the sides of the washer had to be trimmed to fit the locking plastic tabs.
Jets come in 2 different generations. Older metal bases and newer all plastic bases. The all plastic bases are the easiest to convert. Using your kit assemble the threaded rod with 2 nuts and 2 washes to clamp the threaded rod to the base. You can find larger washers to perfectly clamp into the plastic clips and really add to the stability of the socket.
Run your wires through the threaded rod then fix your wires to your intermediate base and screw it in place. You may want to add more nuts to your threaded rod to prevent the socket from spinning when you replace the light bulbs.
There is some wiggle room here to adjust how close the bulb will sit to the base of the Jet globe - just adjust where everything sits on the nipple (seriously, why are they called nipples?!?!) a millimeter or two up or down.
Make sure everything is secure and tight and then snap the top part of the base back on and you're good to go!
You can use a 25 Watt reflector or a 40 watt round bulb. Make sure to watch the flow to determine which is best for your lamp.
Older metal Jets are glued together.
The solution to this problem is to heat up the bottom and start prying from the hole the cord comes out of. Slowly work something flat like a flat box knives around the bottom stopping. Eventually the bottom will pop off.
Take off the metal ring. This will not be reused. On the inside of the base there is a socket that is also glued down. Use your heat to weaken the glue. About 10 minutes later the glue should be pliable enough to pull off the outlet with a pair of pliars.
While the glue was still soft put a washer on a long nipple and push it down in the glue with a screw driver. Assemble your socket like a standard plastic jet and then reattach the base cover.
Astrobabys can be refitted with the same process as the jet. There is some glue around the rim that will need to be heated to remove the bottom place.
Discussions for reference.