I'm working on a project that has similar elements. We receive documents into special email addresses. These documents are processed by Email Archive, Quick Fields and Workflow, then passed to a Forms business process to gather accounting information and approval.
The short answer is that you'll use the "Invoke Business Process" activity to start the process. That said, the activity has a key limitation (at least in version 10, which I am still using). The key limitation is that while you can pass most field information into the process, you cannot pass a document in. Hopefully Laserfiche will add this capability in the near future (if they haven't already added it to version 11).
Like you, we are not able to assign full licenses to every participant in the process, and our participant licenses are the "old" kind that cost less than the ones they're selling now, but that don't allow users even read-only access to a repository.
While I would have liked to pass the document around to users in the Forms process, I used the following two workarounds.
First, for those participants who do have Laserfiche licenses, I configured LF Connector to lookup the document in the Windows client while they have the form open. Since Connector and Windows client both depend on client-side installations working, I also added a link to the form that will let users open the document using the web client. The web client is much slower--due to the need to log in, it takes long enough to annoy most of our users--but will work if they're not on a computer with Connector and Windows Client installed.
Second, for the step to be completed by participants who do not have full licenses, I call a workflow that emails the document to them. (Yes, I know, all you fellow ECM professionals reading this are cringing right now).