Sentry is recommended for error monitoring and debugging in Lambda functions due to its ability to provide detailed stack traces and debugging context. The process of instrumenting a Node function with Sentry involves creating a dummy function, adding Sentry to the Node folder, initializing Sentry in the Lambda function, and wrapping the handler with Sentry's Serverless package. This provides visibility into errors from Lambda functions, including detailed stack traces and helpful function context like aws_request_id and remaining_time_in_milis. With customizations such as capturing timeout warnings and adding breadcrumbs, developers can further enhance their error reporting and debugging capabilities.