The widespread adoption of Machine Learning (ML) across various sectors presents unique challenges beyond the scope of conventional software engineering, especially throughout the lifecycle of ML-Enabled Systems (MLES). As ML becomes central to software operations, the substantial computational resources required for their training, testing, retraining, and maintenance underscore the urgent need for sustainable DevOps practices in AI-centric software ecosystems. Despite the critical importance of this subject, there remains a lack of a unified review that addresses these sustainability challenges within the ML lifecycle from a holistic perspective. This study aims to bridge the research gap by conducting a systematic mapping study of current practices and methodologies that promote sustainable MLOps. Additionally, we have mapped these techniques and methodologies across the MLOps pipeline and extracted lessons learned from each phase to enhance our understanding and application of sustainable practices in MLOps. By doing so, this paper seeks to offer insights into strategies that could mitigate the environmental, economic, technical, social, and individual sustainability challenges associated with MLES, thereby contributing to the development of more sustainable ML-Enabled Systems.