We did some research and here is what we found out:
Almost everybody has a "green" initiative and its deployment varies extensively.
Some organizations (ex. non-profit healthcare) have strong social responsibility components incorporated into their business and the "green" initiative is relatively new, separate from quality assurance of operations.
Sometimes, if there is a Lean Six Sigma deployment, it is leveraged to include and support the "green" deployment and processes.

B Corporations

Some books:
-Green to Gold: How Smart Companies Use Environmental Strategy to Innovate, Create Value, and Build Competitive Advantage by Daniel Esty and Andrew Winston
-Cradle to Cradle: Remaking the Way We Make Things by William McDonough and Michael Braungart
-Natural Capitalism: Creating the Next Industrial Revolution by Paul Hawken, Amory Lovins, and L. Hunter Lovins
-Mid-Course Correction: Toward a Sustainable Enterprise: The Interface Model by Ray Anderson
-The Global Deal: Climate Change and the Creation of a New Era of Progress and Prosperity by Nicholas Stern