The conclusion
After claiming our bags we checked in with LAN for the flight to LAX, which didn't leave for another 10-12 hours or so. My friends all checked their bags, and left my bag (a larger, but still probably legal carry-on size backpack) at the left luggage desk right by the exit to the domestic flights baggage claim ($4 a day). We took a taxi to the Miraflores area of Lima (25 soles) and saw some parks, ate dinner, and generally walked around and people watched. A few hours before our flight we took another taxi back to the airport and waited for a while in the same food court we had been in before, before paying the departure tax and going through security.
Inside the gate area is a single lounge, for all the international flights there. It was okay, I guess, from the 5 minutes I spent inside, with a full bar, a few small snacks, and showers available. But no windows at all that I could see. There was also a small computer area, with internet access (I should mention there is a fairly large internet area accessible to everyone near the food court upstairs with maybe 20 terminals and connection speeds much faster than we had in internet cafes in Cusco or Aguas Calientes - also a little more expensive, but hardly unreasonable).
I should explain now that in our group of four, I was the only one with any kind of status or even FF number attached to my ticket, with my oneworld sapphire (thanks to AA platinum) clearly marked on my ticket (boarding zona preferente!). I should also explain that they are somewhat mystified a little bit by my love of flying and a lot by my stories of life with elite status (e.g. the idea that I could buy a ticket to Japan for a stay of one nights and not only actually get miles worth more that I paid for the ticket but be upgraded on one of the legs for no reason is quite mindblowing). We were sitting in two groups of two, somewhere back in coach. The aircraft for the return trip to LAX was a 767-300, configured with one row of 5 first class seats and something like 24 business class seats. We finally went to the gate area and they called up the two of my friends who weren't sitting with me and handed them business class boarding passes - no status, no request, no reason that we knew of. They were quite surprised (but happy), as was I, standing there with my coach boarding pass (emblazoned with "Preferente"!). They were two of about 10 op-ups, based on the number of names they called. So after waiting a little for the gate agents to finish whatever it was they were doing, I approached with my AA Platinum card stuck to my forehead and demanded "Do you KNOW who I AM?!" But only in my head. I actually just approached with the boarding passes for me and my other friend and asked nicely if they still needed to clear any more seats in economy, making sure they saw the status reflected on my boarding pass, and hopeful but expecting nothing. One agent started to say no, but the other typed a little and then tore up my old boarding passes and handed over two new business class ones, prompting the first agent to tell me it was my lucky day - it looks like we got the last two business class seats, because the cabin went out full. I guess the lesson is to ask nicely about op-ups, perhaps when checking in, perhaps at the gate. If they're going to hand them out randomly to no-status pax who have never flown LAN before, why not ask politely to see if they'll do it for you? (If you paid for business class on the special, I highly doubt they'll move you to first, though, partly because there are only 5 first seats on each plane.)
The 767 entertainment is not as nice as the A340 - no AVOD in coach, and less sophisticated systems even in business. Right after take off they gave everyone a 16.9 oz bottle of Crystal Geyser water, which was great because most people went to sleep right away (and no worries about drinking contaminated Peruvian water). I was asleep before we took off and woke up long enough to recline the seat after takeoff. According to the menu there was a sandwich served sometime after takeoff, but I was sound asleep at that point, I think. Before landing they served breakfast, with a choice of an omelet or crepes. I had the crepes, and they were very good. Incidentally, we got two real metal knives with the meal, and they had real curtains between the cabins - I'm sure any of you would have been as nervous as I was with all those egregious security flaws present, and likely no air marshalls on board.
Despite all that, we landed without incident at LAX around 7:30 or 8:00 am (I can't remember exactly). Everyone on the plane got a little turned around when we came to an alarmed door on the obvious path to the exit, and eventually we all just pushed through and triggered the alarm - they didn't arrest all of us, so it must not have been that important. The four of us dispersed after quickly clearing customs, with two going to terminal 1 to catch flights on WN (which didn't even sound that cheap), one going to terminal 7 to catch a UA p.s. flight I got for him using my miles (I think that guy almost gets the whole miles thing), and me going to my car in my company's garage for the drive back to Santa Barbara. The next day it was back to work to finance my next adventure.