Since there is aditional costs for using HTTP and REST apis on AWS lambda, i would like to know if i could make AWS Lambda receive gets and posts without the need of these HTTP API services.
In this example it seems to be possible:
https://github.com/serverless/examples/tree/master/aws-node-simple-http-endpoint
You will need to use the API Gateway to expose your lambda. Your example is actually using an API Gateway, because the endpoint is execute-api.us-east-1.amazonaws.com and that is the Amazon API Gateway Data Plane.
Just to be clear; if you need to expose the Lambda externally you need to use the API Gateway. If the Lambda needs to be invoked internally then you don't need the API GW.
Best regards