code: def add_lambda_integration(self):
          
          lambda_uri = self.generate_uris()['lambda_uri']
          self.client.put_integration(
              restApiId=self.api_id,
              resourceId=self.resource_id,
              httpMethod=self.trigger_settings['method'],
              integrationHttpMethod='POST',
              uri=lambda_uri,
              type='AWS')
          self.add_integration_response()
          self.log.info("Successfully added Lambda intergration to API")
docs: Attach lambda found to API.