The lease templates is where you can generate the next lease by copying the values from the template, but is you can't create a new lease from a template while in the lease console.

So you can create a template here:
Task: Define Lease Templates
Task File: ab-repm-lsadmin-add-edit-lease-template.axvw
Path: Real Property/Leases/Background Data/Define Lease Templates
that is where you can get an existing lease it copies it changes it into a template for you

Then to apply the template to a new lease you would go to
Task: Portfolio Edit Form - Complete
Task File: ab-repm-addedit-lease-form.axvw
Path: Real Property/Leases/Lease Portfolio/Portfolio Edit Form - Complete

It would make sense to have this functionality also appear in the lease console since that was the one stop shop.