Can you convert newer accessories that support iPhone 5 back to iPhone 4?

My mum is getting a new ipod dock for her birthday and it's one of the new ones so it has the lightning pin in it, but she has an iPhone 4 so she needs a converter.

I know you can buy an adapter to go from iPhone 4 > iPhone 5, but does anything exist that converts back from new to old? I've looked everywhere and I don't think they exist.

What you want is not available and never will be. To adapt Lightning to Thunderbolt would require more than just a simple pin adapter; there would have to be an electronic dongle and suitable firmware as well.

Given that there are still loads of products made which natively accept Thunderbolt devices and that users of Lightning would not want to pay extra for a function they don't need, and that Thunderbolt is rapidly dying out as users upgrade their phones, it makes no economic sense for any manufacturer to produce them. In any case both connectors are proprietary products which Apple holds the patents for and they would sue anyone using their technology without permission.

Your answer is simple: cancel your order or return the goods and buy a suitable replacement, or add an iP5 to your Christmas shopping list.