### Is there an existing issue for this?

- [X] I have searched the existing issues

### Current Behavior

I Created an REST APIGatway with lambda handler using AWS CDK. when I hit the API the response header content type is always  set to "text/html"  instead of `application/json` . even if I changed the response template or added the header to lambda returned response. when I deploy the same stack on AWS account  the response header is fine and work as expected

### Expected Behavior

Response Header content-type to be `application/json`

### How are you starting LocalStack?

  `localstack start` command

### Steps To Reproduce

#### How are you starting localstack (e.g., `bin/localstack` command`)

    `localstack start` command

#### Client commands (e.g., AWS SDK code snippet, or sequence of "awslocal" commands)

I'm using AWS CDK typescript application and deploy it using `cdklocal` command on localstack

Using CDK follow the steps:
- create  REST ApiGateway
- create Lambda function 
- integrate lambda with APIGatway

On Command line:
- deploy using `cdklocal deploy` command

Finally
- test the endpoint and check the response header content-type




### Environment

```markdown
- OS: Windows 
- LocalStack: latest
```


### Anything else?

When I deploy the same stack on AWS account everything works fine and the response header content-type is `application/json`
"""
    Simple class to mimic the behavior of variable '$input' in AWS API Gateway integration
    velocity templates.
    See: http://docs.aws.amazon.com/apigateway/latest/developerguide/api-gateway-mapping-template-reference.html
    """
    def __init__(self, body, params):
        self.parameters = params or {}
        self.value = body
    def path(self, path):
        if not self.value:
            return {}
        value = self.value if isinstance(self.value, dict) else json.loads(self.value)
        return extract_jsonpath(value, path)
    def json(self, path):
        path = path or "$"
        matching = self.path(path)
        if isinstance(matching, (list, dict)):
            matching = json_safe(matching)
        return json.dumps(matching)
    @property
    def body(self):