I agree the better analogy is that software itself is the factory. We should aim to create lean software (well factored into simple, reliable, modular component

I agree the better analogy is that software itself is the factory. We should aim to create lean software (well factored into simple, reliable, modular components dealing with manageable chunks of data at a time). Lean manufacturing doesn't really imply much about the day-to-day work of the factory designers and their interactions with their stakeholders, except to say that when bugs (or inefficiencies) happen a developer should fix them to get the "factory" moving again. Which is a different story to "how do you design a greenfield factory?" and "how do you design the widgets produced by the factory that will entice consumers to buy them?" and many other important aspects. If we compare to Toyota, your software team is responsible for designing the cars, building a factory from scratch for said cars, running the factory and getting cars out the door, improving the cars based on consumer feedback, improving the factory based on bugs/inefficiencies/internal feedback, while making all of the above profitable. It's a whole range of responsibilities and tasks that need to be managed differently.