I'll start this discussion by weighing in myself. I am coming to believe that a large OTV is entirely doable and would be of sufficient size to satisfy future market demand for lunar-derived LEO fuel. Constructing the OTV would require nothing larger than Falcon 9 Heavies. In other words, for a reasonable cost, an OTV could be developed and in a few years from the word, "Go". I also understand that such an OTV would also be able to serve as a lunar lander, delivering significant payload (i.e. lunar ice harvesting equipment) to the lunar surface. In other words, develop the OTV and you can have the entire LITL system. The return on investment would probably be pretty good.
So, why would we need a smallish LITL system -- one which could be demonstrated in principle using a single or perhaps a pair of F9Hs? The only reason that I think that we would need to do such a thing is if, after the prospecting mission, investors for the full LITL system didn't emerge and/or if NASA was unwilling to spend the money to help that system be developed (e.g. a "Lunar COTS").
So, my feeling is that we could determine whether a LITL demo was necessary some time shortly after the prospecting mission as we see whether investors or NASA are willing to go to the full LITL step. If not, then I think that a LITL demo could be the thing that could "seal the deal" by demonstrating that a LITL system works and that there's a market for it.
The OTV would transport the equipment to the lunar surface. It would then ascend back to LEO where it would refuel from another launch for this purpose. It would then return to the Moon where it would have enough fuel to bring back some ice. In other words, in the demo, there would be no cracking of water into fuel either at the Moon or at LEO in order to simplify the mission and yet still demonstrate what such a system would look like. The emphasis is on returning lunar ice to LEO not cryogenic handling. There would also be no demo of telerobotic repairs.
The equipment would teleoperatically harvest and distill water from ice at locations found during the Prospecting Phase. Steamed water would be collected in the OTV's cargo hold (no need for a separate container for this). With enough fuel, the OTV now ascends and does aerocapture to LEO. Ideally it would deliver this "drinking water" to the ISS, a Bigelow module, or a fuel depot if such existed at that point in time. For about $300 million in transportation costs plus development (useful for full development) and operations, one could provide a fairly convincing demonstration of the overall LITL system.
With that equipment in place, perhaps stores of purified water could be built up on the Moon and LEO until something breaks and work ends.
The nine launches includes lifting the processing equipment. My idea for a L-1 depot is to modify a couple of the F9 second stages to act as a depot.
Yes. ULA proposed the same thing with Centaur upper stages - I don't see why SpaceX couldn't make a few second stages to order when we get that far with them. Of course, it would require that they use the Raptor engine for the upper stage; that would give us LOX and LH tanks and related systems.