I had a very similar problem with my auto LX, I would make a turn and the engine would die but start up right back again. Oddly enough i happend to fix it by changing my spark plugs...i don't really see the connection but when i pulled mine, the gaps were way off. But that's the only thing i did and my car stopped dying on turns?!? You might want to check the gaps on your plugs?

I had that exact same problem and I went nuts trying to firgure out what it was.
I went through the entire fuel system, electrical, and engine, but still nothing. Finally after many replaced parts it still stalled when turning right. I was about to get rid of the car but I tried one more thing, the fuel filter.
After that it ran great again, and I couldn't believe the little fuel filter was causing big problems:p

I had exactly the same problem. I removed the fuel pump and sending unit from the tank and the strainer was filthy dirty - only had about 15% of its surface area left that would allow fuel to flow. Then I removed the strainer and cleaned it up with some degreaser. You can use white wall tire cleaner or any degreaser detergent. Then I rinsed it with aerosol brake cleener and re-installed it. Car runs great now, I can take highway ramps and tight turns at speed with the low fuel warning light on and there is no hesitation. If you're not cheap like me, you can just replace the strainer for about $20.