Does the Lexus engine have an Idle Air Controller as I suspect it does? Mounted on the throttle body, the IAC meters air into the engine at idle when your foot has not opened the butterfly valve via the accelerator pedal. When the IAC valve gets stuck from being dirty, it can cause symptoms 1, 2, and 3. Not sure about symptom #4, have you checked your upstream (closest to the exaust manifold) 02 sensor which when it goes bad, can cause a dramatic loss of performance and fuel economy?
Also check and see if both coils are good!