Lean manufacturing and the Toyota Production System are absolutely about manufacturing. It's rooted in industrial engineering and operations research. It is about addressing root causes and truly solving issues. What we see in the lean books is a bunch of solutions to problems Toyota was facing at the time and how they solved them.

Even the person who coined "lean manufacturing" says, "Don't try to bring lean manufacturing upstream to product development. The application of Lean in product development and manufacturing are different. Some aspects may look similar, but they are not! Be weary of an expert with experience in lean manufacturing that claims to know product development."[1]

There are a couple of books that have tried to capture the design process from Toyota. [1] is the Wikipedia page for [2]. [3] is an alternative take. Unfortunately I haven't read these books, so can't provide anything beyond the table of contents.

[1] https://en.wikipedia.org/wiki/Lean_product_development

[2] the table of contents needs to be downloaded from https://www.lean.org/store/book/lean-product-and-process-dev...

[2] https://www.routledge.com/The-Toyota-Product-Development-Sys...