OP has two separate problems:

1. Getting to LIM. He's been told that there is no availability for 6 days. That might even be true given that it's high season with a good economy.

2. Preserving his ticket. AA, as with all of the US carriers, is pretty decent about rebooking even when someone has missed a flight and the rules say that the ticket has no value. But, OP is at the bottom of the barrel in terms of priority and AA won't rebook OA where it costs AA money to do so.

3. OP is booked through Expedia and it appears that he has not started his journey. AA is properly referring OP to Expedia. Expedia will stick to the "letter of the law" and impose its own terms above and beyond. That could well mean no rebooking and purchasing a new ticket. For this reason I would not call either AA or Expedia. When OP gets to LHR, he should go to the AA counter and plead his case. AA can either help or not because of the Expedia-issued ticket. But, the circumstances will be apparent. Repeated phone calls only result in confusing PNR notes which make the counter agent's work harder and thus less likely satisfactory.

4. It's unclear to me what OP's onward LAN routing is about. But, that is a different story and sorting with LAN, if need be, may be problematic or not.

Water under the bridge for OP, but this is yet again another example of why booking through opaque third-party vendors is a risk. While the HEX doesn't hit someone every day, bad things happen regularly. When booked through the operating carrier, fixing problems can be readily -- if not satisfactorily -- handled. When booked through a third-party vendor, life can be difficult.

Insurance is always a backup here and OP should call his insurance to let them know what has happened. But, whether he needs it or can simply get rebooked won't be apparent until he speaks with a counter agent at AA when he is physically at LHR.