UPDATE-- since the last cutoff issue 3 weeks ago, LX has been running great. Maybe the fuel pump relay was the cure. ALmost 16 MPG on a 50 mi trip.
Was the fuel pump relay the fix? if so, which one?
I went through the exact same thing last night. I was on a 3 hour trip and it started doing it after the first 30 mins in. I immediately found this thread. I started looking for all the details, cutting off the lights and radio, with the Ac on and off, watching temps, etc..
It did it without flickering the lights or the radio when it started, but as it got darker, I noticed the lights did flicker and so did the radio. The clock never reset itself though. It kept the time. It did it like 6 times in an hour. Then stopped doing it for another 1.5 hour then one more time right before I got home. I didn't have to restart the vehicle, it would re-start itself immediately. I did change the alternator like 2 months ago. I'm going to go in there and check all the connections.