The correct service is Amazon EKS (Elastic Kubernetes Service), as it allows for the deployment, management, and scaling of containerized applications using Kubernetes on AWS without the need for the user to manage the Kubernetes control plane themselves. Amazon ECS (Elastic Container Service) also provides a managed container service but is not specifically tailored for Kubernetes, which is hinted at by the mention of open-source orchestration in the question. AWS Lambda is designed for serverless workloads, not for managing containerized applications with Kubernetes, and launching EC2 instances would require manual setup and management of Kubernetes, contrary to the 'fully managed' aspect mentioned in the question.