Hi Hugues,
I have been involved as an LSP facilitator with startups a few times.
Business modelling is of course a major issue, but in my experience so is product definition. Beyond the obvious agreement on superficial aspects, team members tend to have even wildly differing notions as to the hows and whys of the product.
This usually remains hidden underground until it surfaces as a development issue.
LSP is of great help in building a shared understanding of core product aspects.
Also, team relationship issues tend to pop up early when tackled through LSP.
The usual startupper approach is “we are a group of peers” until it transpires that somebody specific needs to be held accountable for something. And somebody must actually deal in person with financiers. etc.
All things being equal, building a shared understanding of how and why the organisation seeks money is what makes the difference between a bunch of guys with an idea and an actual investor-worthy startup. IT people, in particular, have specific difficulties you have to deal with. I know, one of my cards reads “post-autistic-IT therapist”
I also have used the Agile Canvas together with LSP for the business model part.
Let me know if there is something I can do to help.
Cheers, Walter