Elastic's Infrastructure team has implemented a serverless approach to running Elasticsearch Curator on AWS Lambda to reduce management overhead and increase efficiency. Instead of using servers, they employ serverless computing to handle tasks related to storing and analyzing system metrics, logs, and performance data using Elastic Cloud and Elasticsearch clusters. The process is facilitated by Lambkin, an open-source tool that simplifies creating, publishing, and scheduling Lambda functions. The setup involves configuring AWS credentials, creating a skeleton Lambda function, and using Python to develop the function, which can be managed and scheduled to run regularly using a YAML configuration file. This method allows the team to maintain a reliable, scalable system without expanding their server infrastructure, and the entire setup can be easily modified or checked into version control for future updates.