Still haven’t figured this out and I’m afraid my sister my have to take the car to a paid professional! Here’s what I’ve tried:

Replaced cam position sensor
Replaced IAC motor
New spark plugs- old ones had 40k miles and were black & oily
Replaced fuel filter
Replaced fuel pump relay
Checked for vac leaks

Figured out that it was running loud because the exhaust broke at the cat- probably from the engine running rough & shaking.

After each of these, it would not start. It doesn’t seem like a fuel issue, because I can hear the pump running with the key on and I’ve got pressurized fuel when I crack open the connection at the fuel rail. I read that the cylinder walls might be getting washed with fuel and lowering compression, so I decided to dump a tablespoon of oil into each of the spark plug holes and do a compression test at the same time. I got 85, 85, 95, 75, 95 at first and 165, 180, 165, 150, 170 after dumping in the oil. The car fired up and idled fine after that! I hoped that one of the things I had done fixed it and my sister drove it on her 10 mile commute for the next 2 days with no problems. On the third day, it started acting up again- the Lambda light came on and it would idle rough unless it was put in park. Eventually it stalled and would not restart.

I was thinking about replacing the coil, plug wires, and maybe the TPS before giving up. Any other ideas?