Monitoring AWS Lambda functions effectively involves understanding and tracking key metrics such as invocation, performance, and concurrency metrics to identify and address potential issues. The process includes using Prometheus to collect metrics from CloudWatch and forwarding them to Logz.io for scalable storage and analysis, allowing for unified monitoring and troubleshooting with log analytics. By setting up dashboards and alerts in Logz.io, teams can visualize and manage their Lambda metrics more efficiently, with alerts notifying users of issues like increased error counts. This setup streamlines the process of correlating metrics with logs, enhancing the ability to debug and resolve problems swiftly. The choice between using Prometheus or Logz.io for monitoring depends on a team's resources and preferences, with Logz.io offering a managed service that unifies metrics, logs, and traces in one platform.