The Pulumi team faces challenges in managing cloud costs due to the necessity of accessing multiple cloud providers for product development and testing, which can lead to uncontrolled cost increases when developers fail to properly clean up resources. To address this, Pulumi leverages an AWS Lambda Go application to automatically remove unnecessary cloud resources daily, using tags to track resource ownership and prevent deletions. By employing Pulumi and AWS Lambda, the team can monitor and reduce costs effectively, as demonstrated through a detailed process of deploying a cloud cleanup solution targeting unattached EBS volumes. This solution involves creating a lambda function with specific roles and policies, deploying it across multiple AWS regions, and iterating on the application to achieve significant cost savings, reportedly reducing daily AWS expenses by 64%.