Do cheap iPad Lightning to USB camera adapters work?
The reason the adapters from apple have such a high price is because the product have a chip inside that will make sure the product keeps working. Cheaper product often don't have such a chip. It is possible that those products work, but they can stop working at a random time.

There are products from other companies that are also supported by apple because they pay a licence to develop such products.

Every product that has the "made for iPod, iPad and iPhone" logo on it's cover are supported by apple.