Scenario: I create 4 different lambda functions using docker images. Each function is created froma separate image. Each function contains different FAST API routes for a different service.

I create an API Gateway and invoke the 4 different lambda functions with proxy integration. For each, I create a resource and method ANY. All lambda functions are created in the same account, same vpc and same security group. I create another lambda function from a docker image. This function make call for different routes in the API gateway.

I create a resource policy for the API gateway:

{
  "Version": "2012-10-17",
  "Statement": [
    {
      "Effect": "Allow",
      "Principal": {
        "AWS": "arn:aws:iam::account-id:role/Lambda-5-Role"
      },
      "Action": "execute-api:Invoke",
      "Resource": "arn:aws:execute-api:us-east-1:account-id:api-id/*"
    },
    {
      "Effect": "Allow",
      "Principal": "*",
      "Action": "execute-api:Invoke",
      "Resource": "arn:aws:execute-api:us-east-1:account-id:api-id/*",
      "Condition": {
        "IpAddress": {
          "aws:SourceIp": [
            "x.x.x.x",
            "y.y.y.y"
          ]
        }
      }
    }
  ]
}

The Lambda-5-Role contains:
AWSLambdaBasicExecutionRole, AWSLambdaVPCAccessExecutionRole, CreateNetworkInterface-policy permissions and the following permission:

{
    "Version": "2012-10-17",
    "Statement": [
        {
            "Effect": "Allow",
            "Action": "execute-api:Invoke",
            "Resource": "arn:aws:execute-api:us-east-1:account-id:api-id/*"
        }
    ]
}

When I test it, I got :

{
  "Message": "User: anonymous is not authorized to perform: execute-api:Invoke on resource: arn:aws:execute-api:us-east-1:account-id:api-id/stage/method/route"
}

It is working well without resource policy. What is the mistake that I am doing ?