It looks like a duplicate of old issue https://github.com/localstack/localstack/issues/78
But now it's reproducible for me with the latest version of LocalStack. 
apig.delete_authorizer(
            restApiId=self.TEST_API_GATEWAY_ID,
            authorizerId=authorizer_id)
        self.assertRaises(
            Exception,
            apig.get_authorizer,
            self.TEST_API_GATEWAY_ID,
            authorizer_id)
    def _test_api_gateway_lambda_proxy_integration_any_method(self, fn_name, path):
        self.create_lambda_function(fn_name)
        
        lambda_uri = aws_stack.lambda_function_arn(fn_name)
        target_uri = aws_stack.apigateway_invocations_arn(lambda_uri)
        result = self.connect_api_gateway_to_http_with_lambda_proxy(
            'test_gateway3', target_uri, methods=['ANY'], path=path)
        
        path = path.replace('{test_param1}', 'foo1')
        url = INBOUND_GATEWAY_URL_PATTERN.format(
            api_id=result['id'], stage_name=self.TEST_STAGE_NAME, path=path)
        data = {}
        for method in ('GET', 'POST', 'PUT', 'PATCH', 'DELETE', 'OPTIONS'):
            body = json.dumps(data) if method in ('POST', 'PUT', 'PATCH') else None
            result = getattr(requests, method.lower())(url, data=body)
            self.assertEqual(result.status_code, 200)
            parsed_body = json.loads(to_str(result.content))
            self.assertEqual(parsed_body.get('httpMethod'), method)
    # =====================================================================
    # Helper methods
    # =====================================================================
    def connect_api_gateway_to_kinesis(self, gateway_name, kinesis_stream):