How to re-route in API Gateway in Lambda REST Api?

Question

I have a REST API with these resources:

/Api/Customers 
/Api/Orders

I have a front end app that needs to call these resources. I want to use front-end specific routes. I have an API gateway in between these two services. How can I re-route the frontend requests to a backend lambda REST API?

/outsideworld/Customers -> /Api/Customers
/outsideworld/Orders -> /Api/Orders

If I select HTTP as the integration type I see a way to route to a "Endpoint URL". However, if I select LambdaFunction I don't see that option.