Critical to the development of a learning organization is a system approach. Dysfunctionally homeostatic systems seem to survive in spite of themselves. I can think of any number of organizations operating in a response mode which would fall neatly into this category. The twin-headed evil which seems to exists in business today goes by the names of arrogance and complacency. But I don't know that I would say these organizations are evolving.
Evolution is a natural response to environmental influences.
Perhaps, then, a healthy system evolves to a learning organization through genetic engineering.