I suspect if there was an outbreak of people getting sick after flying LAX-ITO, this would be bigger news than this thread.

Perhaps it's something to do with your sleep and hydration patterns for that trip? A very long westbound followed by another medium-haul flight isn't something I've personally done a lot of, but it sounds more taxing on the body than most of my itins where the long-haul is usually followed by a hotel room.

If you were traveling somewhere more exotic I might think it was a normal ingredient in the destination's food or water that is disrupting your foreign stomach. But that doesn't seem as likely with LHR, LAX, or the airline catering in those two places.