Trigger a lambda function after a rest api is accessed

Question

I use a rest API in the Aws api gateway to retrieve data from an external http endpoint.

I need to start a lambda function that consumes the data supplied by the rest api every time this rest api is accessed and returns data. How can I go about doing that?

I've tried searching for answers, and every single one of them points to the use of a rest API to start a lambda function.