Which action would help the developer troubleshoot this issue?

Explanations:

The IntegrationLatency metric measures the time taken for the API Gateway to receive a response from the integrated backend (in this case, the Lambda function). While it can provide insights into the performance of the integration, it does not directly address whether the Lambda function is taking too long to execute or is timing out. Therefore, it may not help diagnose the root cause of the timeouts.

The Duration metric for the Lambda functions indicates how long the functions take to execute. If the functions are timing out, this metric can help the developer determine if the execution time exceeds the configured timeout, which is critical for troubleshooting the issue. Monitoring this metric allows the developer to identify performance bottlenecks or issues within the Lambda functions.

The Count metric of the API in CloudWatch shows the number of requests made to the API. While it can provide insights into the usage of the API, it does not give any indication of performance issues or timeouts occurring during request processing. This metric alone cannot help troubleshoot why responses are timing out.

The Errors metric for the Lambda functions indicates the number of errors that occurred during function execution. While this is useful for identifying if the functions are failing, it does not directly address whether the functions are taking too long to execute, which is necessary for diagnosing timeout issues. Therefore, it may not provide the specific insights needed for troubleshooting the timeout problem.