AWS Lambda offers a serverless, event-driven service that simplifies infrastructure management by executing code automatically, allowing companies to focus on scaling and prototyping without managing servers. Users pay for compute time, thus requiring efficient monitoring to avoid unnecessary costs. Memory allocation significantly impacts Lambda performance, with potential issues like cold starts, execution time limits, and concurrency limits affecting efficiency. Continuous monitoring, beyond AWS's basic tools, is vital for detailed insights into function behaviors, helping troubleshoot and optimize performance. New Relic provides comprehensive Lambda monitoring, offering detailed invocation data, event information, distributed tracing, and contextual logs, enhancing operational efficiency and cost-effectiveness.