Yes, AWS Lambda automatically monitors Lambda functions on your behalf, reporting real-time metrics through Amazon CloudWatch, including total requests, account-level and function-level concurrency usage, latency, error rates, and throttled requests. You can view statistics for each of your Lambda functions via the Amazon CloudWatch console or through the AWS Lambda console. You can also call third-party monitoring APIs in your Lambda function.
Actually we use cloudwatch as the main tool for these purpose.