okay like he said above solve one problem at a time, it might fix the other issues. the lexus is a very complex beast and two things that u would think have nothing to do with each other seem to coincide. first and foremost. disconnect that fuel pump wire from the headlamp fuse. then check the connections at the pump itself. if its plugged in, go to the fuel pump ECU located in the arm rest panel on the driver's side in the back seat. make sure the ecu is plugged in. small silver box with fins on it. attempt to start the car. if u get a no start, disconnect the fuel pump ecu and take the two larger gauge wires from the harness and plug them into each other. attempt to start the car. this bypasses the ECU the proper way. it also ensures u have constant power with the vehicle in run mode, and the proper amperage and voltage. if u get a no start that way, check to make sure ur fuel pump fuse is still intact. after that ur car should be running. then check ur other issues. private message me if u need more help.
A million thanks. After I get done following those steps, I'll PM you and let you know the results