AWS Lambda execution lifecycle consists of three main phases: initialization, invocation, and shutdown. In the initialization phase, a Lambda creates its runtime environment, downloads code, imports necessary modules, and runs initialization code. During the invocation phase, the Lambda processes an input, produces output, and waits for the next input, eventually moving to the shutdown phase after idle time exceeds a threshold. To add capabilities beyond these phases, AWS provides Lambda extensions, which can be categorized into external and internal extensions. This response will focus on using external extensions. An example use case is building a cross-runtime log shipper without modifying the Lambda function itself. External extensions enable registering events for specific phases and sending HTTP requests to AWS to register and complete tasks. The process involves storing a unique identifier from AWS, waiting for the next phase, and informing the extension name to AWS. Solutions like lambda-log-shipper provide pre-built implementations of log shipping and other use cases, allowing developers to easily get started with extensions without implementing everything by themselves.