I don't understand the benefit of that. Could you explain please? It sounds to me like doing what you describe would prevent all the wins of serverless - scaling and only paying for the runtime you use. In what you describe, you get zero auto-scaling unless you implement it yourself, and you pay more than just lambda or just a http server. It sounds like adding another layer of complexity on top for no benefit
I think the idea is to run a regular http server locally that forwards requests to your lambda handler function for the purpose of testing. When you actually deploy your lambda, you just hook up the lambda handler function and leave the http server out of the picture.