Something to consider: I don't know much about about Laura, but I anticipate my perspective on the subject to be slightly different from those two books in that I worked as an ACD/Copywriter on LeanUX and Agile Dev teams in a startup, and was in charge of maintaing the brand. (We noticed early that the brand was going to suffer using Lean if we weren't careful.)

That's where we developed my version of Lean Branding, so I assume it's a little more in the trenches and focuses more on the day-to-day building and curation side, and (total assumption) may be more actionable. I think they both approach it from more of a strategy perspective.

(These are assumptions based on observations, and I'm not saying either perspective has more value, just that they're likely going to be different.)