Sustainable software development, deployment, and usage will minimize the burden on the economy, environment, and technology along with having positive effects on human beings, and society. Green and Sustainable Software Engineering processes, principles, and practices provide the basis for sustainable software development. However, the continually increasing customer choices and requirements, environmental concerns, and competition among software development industries demand for the availability of reliable and complete sustainable software development approaches to develop lifelong sustainable software. This paper presents a sustainable software engineering framework, named as LAGSSE, by integrating the Agile, Lean and Green approaches. The framework is based on the “OntoSuSD” ontology to represent the diverse Agile, Lean and Green approaches for achieving the software sustainability dimensions, goals, and enablers. The proposed framework is validated using the Delphi method using the expert opinion scenario which has proved LAGSSE as an efficient framework for supporting sustainable software development. The LAGSSE framework is aimed to facilitate the software developers, academia, experts, and policy makers in the software industry, institutions, and government to make policies and develop sustainable software products according to their software sustainability goals and requirements.