I find that once "ROI" is requested, the person asking is more concerned about the "I" - how much is this gonna cost me? As most people have already stated, Lean has more to do with the long-term changes and benefits, and not one specific project's financial metrics.
But that doesn't solve the problem of getting asked to do an ROI, and executives in most business are conditioned to evaluate cost/investment first. That's a great task for the CFO's team: what will it cost and do we have the money, where does it fit into the budget planning, etc.
Continuous improvement and Lean engineers or managers have a different task: focus on the "R".
No executive wants to hear things like "I need $15,000 for a project and I estimate it will save $30,000". Immediately they wonder, what if it saves less, or it takes too long, or costs more? That sets up plenty of doubt and scrutiny.
But if someone approaches an executive with "I can bring you 30% more sales" they might respond with "where's the PO?" or "over what time period?" and the discussion will take a path focused on money coming in, not going out ("R" instead of "I").
Cost saving and cost reduction is not a return, as most people consider it. First of all, you can't save cost. You can "save" money by taking it from one place and moving it into another instead of spending it. You can reduce cost by paying less for things, but that's not a return...you're not creating anything new. In business, if you pay less for things, but less money comes in at a higher rate, you're not better off.
Return is when your action (project, etc) creates new money coming in that wasn't there before. If you spend 1 million to earn 1.5 million, that's a return of half a million in new money. If you spend 1 million to reduce spending somewhere else by 1.5 million, there's no return...you just reduced expenses by half a million.
In the cost accounting world, I might be banned from ever posting again because clearly, I don't understand the math. But cost accountants are happy to see flat sales and declining costs - "hey our margins are kicking butt!"
That's great, if sales are guaranteed. But how much can costs decline? Eventually that trend bottoms out. You need to pay for people and material and the facility you're in, not to mention taxes! There's a lower limit in that equation. Which means the "ROI" has a finite upper limit.
So when an executive says "what's the ROI on Lean?" the answer is "if sales are a constant, the maximum ROI is X, based on the minimum achievable cost to maintain that sales number." If you do real quick math, the minimum cost can be guesstimated pretty close. And that's the BEST outcome you can hope for, meaning Lean has an expiration date for you.
The other (BETTER) approach is figuring out "what's the most we can sell?", and allowing Lean to be your strategy to go get it. That's a much better analysis because the size of the market is essentially the upper limit on sales, and understanding what the market VALUES is the critical step. The rest of what Lean has to offer - the fun stuff like Flow and Pull - can be applied to meet the new demand and keep COST flat (aside from the variable costs like material to produce new volume).
The ROI on those efforts is 5X, 10X, maybe 100X the ROI of the alternative maintain-sales-and-reduce-costs approach.
A project with 100% ROI sounds great, but if that means spending 1,000 bucks to reduce spending by 2,000 bucks somewhere else...eh, I'm not that excited. Even if the project is executed flawlessly, what's the cost of people's effort to make it happen? That effort, if focused on GROWING the business, is worth far more than 100% ROI.
I said a lot, and others have said similar things. But I lived this, and saw how a simple change in approach made all the difference in the world for the company (and for my career). You can read my story here (if the admins are OK with it): https://www.dropbox.com/s/m8x6m6b31pono8j/MyLeanCaseStudy.pdf?dl=0