The short answer is: yes!
Friendship Lamps (and new Friendship Frames) work anywhere with Wi-Fi. So if you're wondering, "Will they work if I'm in the US and I send one to the UK?" have no worries! If there was Wi-Fi and a power outlet on the moon, then you could have a Friendship Lamp up there.
Friendship Lamps work by connecting to the internet to talk with their group. They will work the same way if you have them both connected to the same Wi-Fi signal as they do working thousands of miles apart.
They do come with US (Type A/B) plugs though, so if you're looking to connect them internationally you may need to get a plug adapter. They are dual voltage, so you won't need a pricey voltage converter, just the adapter (which should be pretty cheap)!