The rapid integration of Cognitive Digital Twins (CDTs) across various industries has revolutionized operational practices, leading to enhanced efficiency and improved decision-making capabilities. However, this technological advancement is accompanied by significant environmental implications, particularly regarding the management of electronic waste (e-waste) and digital waste. While e-waste primarily concerns the disposal of obsolete hardware, digital waste encompasses inefficiencies, redundancies, and unnecessary consumption of computational resources in the digital environment. This paper emphasizes the importance of understanding the lifecycle impacts of CDTs and advocates for the implementation of sustainable practices in their management. To address these challenges, we introduce Digital Twin Portfolio Management (DTPM) as a systematic framework for optimizing the CDT ecosystem. We also present the Digital Twin Triple Bottom Line as a framework for assessing the technical, economic, and environmental impacts of CDT implementations, ensuring that organizations can identify inefficiencies and align their operations with broader sustainability objectives. The findings elucidate the various types of waste generated by CDTs, establishing a critical link between digital asset management and environmental sustainability. Additionally, the study advocates for improved APM practices tailored to the unique challenges posed by CDTs, contributing valuable insights to the evolving discourse on IT portfolio management. Future research directions are also discussed, including the need for expanded case studies and longitudinal investigations to enhance the generalizability and understanding of CDT lifecycle management.