To your question about how do consultants "do" Lean:
From the purists perspective it is a strategic methodology that initially requires understanding the 'current state' which requires documenting a map including process steps, people required to the work, WIP, etc (see Learning to See by Rather and Shook). -This map then becomes the guide for developing the 'future state' and prioritizing Kaizen events usually in one service (an inch wide-mile deep).
-Simultaneously, the organization chooses key individuals across the entire company to go through Lean training (modules, quizzes, fundamental tools-See Mark Hamel's Kaizen Fieldbook- An Excellent Resource).
-The consultant guides these individuals through the training, and also begins to teach executives how the tools will highlight the improvements in Cost, Quality, Safety, Delivery & Morale. These tools focus on the elimination of waste: time, transport, defects, inventory, overproduction, processing, & motion. Furthermore the C, Q,S, D, M are tracked & trended after each Kaizen event to measure improvements, transparency & accountability and posted in a room where each leader should be required to speak to their metrics weekly/monthly/quarterly and point out why it is going well, or not.
-There are a series of milestones the company should meet before introducing further concepts (3P, Hoshin Planning, Lean Accounting), but ultimately the goal is to transfer all the knowledge to the organization and create a Lean Enterprise over 3-5 years.
-Many companies struggle with the commitment or have a short attention span and lose focus, but the pay-off is extraordinary. Obviously, look at Toyota :)
-Also, several try to fit Lean and Six Sigma in the same box and although they are complementary, Lean must be used first to stabilize and develop repeatable processes before Six Sigma can do its work of process control. Six Sigma often focuses on 'projects' as where Lean should be a 'culture' change.
Working in Lean from the Shingijutsu training has been a wonderful experience and allowed me to work in a multitude of industries. If you would like to pick more of my brain, I am always happy to share.
Hope this was helpful.