AWS Lambda is a serverless event-driven service that automatically executes code to deliver the right AWS resources for your infrastructure without management, paying a fee for the compute time used. To get detailed performance data and avoid overpaying, continuous monitoring is necessary, which can be complex given the distributed nature of Lambda functions. Memory usage affects Lambda performance, with allocating too much memory leading to throttling and poor concurrency limits. Common issues include large functions, cold starts, execution time limits, and concurrency limits. To troubleshoot and improve Lambda performance, a third-party continuous monitoring solution is necessary, providing detailed information such as invocation criteria, error analysis, and a single view of all Lambda functions in every AWS region. New Relic offers full Lambda monitoring with features like invocation tracking, events, distributed tracing, logs in context, and inventoried tags and metadata, to help optimize performance and costs.