I went a step further and replaced the rear passenger sensor in my 2001 LS430. I couldn't find any pictures of the installation, so I figured I'd take some and post them here since this thread was so helpful in replacing the front passenger for me. The only thing I had to add to the instructions on removing the front passenger oxygen sensor was that removing the giant front plastic pan that covers the entire engine area from the bottom allowed for the right angle to unplug the sensor. After spending an hour (or two) trying to get it undone AFTER already figuring out the clip part, I just couldn't get it to slide out. Once I removed that panel, it slid right out for me!
The rear passenger sensor is attached right to the exhaust pipe and doesn't require the oxygen sensor socket to remove so you can use just an open wrench. I did have to apply penetrating oil as it was quite stuck and I didn't want to pry too hard on the exhaust system for fear of creating leaks. I gave it a good hour (or two) while I worked on the front passenger sensor which is detailed above.
So now that the penetrating oil has done its work, I removed the sensor from the exhaust with the open ended wrench. The photo below shows where the sensor came out along with the new sensor as I took this photo closer to the end.
Now we move inside the car into the passenger foot well. To find where the wire came through the floor I poked my finger up in the hole while under the car. My wife, who was in the passenger seat area watched for where the floor was coming up. It basically comes through in the left front corner of the foot well.
We determined that based on the drawings in the original post from the Lexus manual, the intention was to remove the air vent to gain access to where the connection is. To remove this vent, pull out from the side that is towards the rear of the car, this will release the build-in clip, and then slide the cover towards the rear of the car to pull the tab out of the slot.
Now you can pull the carpet out to the left and the right of the vent as you can see in the photo below. The wire travels from the front left corner of the passenger foot well until it reaches the vent height, and then takes a 90 degree turn towards the back of the car. When you first reach your finger in youíll find it just below the vent. Towards the rear of the car, to the left of the vent is where it clips into the wire harness.
Unclick the white clip here with the top toggle and it should come out easy. The white clip is pictured below:
Towards the front of the car, to the right of the vent, there is a clip that holds the wire to the plastic frame which you will need to remove. Squeeze the tabs on the back and then pull it through the hole, should be easy to remove. Iíve included a photo below which shows the oval hole after the clip was removed.
Now that I had the whole thing disconnected, I decided that I would put the new wire in before removing the old. I figured that if I couldn't get the new one in for some reason, it would be bad to take the old one out. So I took the new wire and used the wire tie that came with it to tie the rubber outer layer of the wires to the clip on the end of the wire. This prevented the outer rubber casing from getting bunched up while I slid it through hole and under the floor. From under the car I fed it through the hole while my wife put her hand down behind the carpet around the air vent from top side. She managed to grab the end of the wire and pull it through and plug it in.
Now secure that we had everything through set as far as wire fishing, we wrapped the clip on the end of the old wire with electrical tape to prevent it from getting snagged and I pulled it through the hole under the car while my wife guided it through the carpet. At the end it got stuck, but I gave it a good tug and it came through. With the old oxygen sensor now entirely out, we applied the anti-seize compound to the threads and screwed it in. I then pulled the rubber casing down the wires to cover the wires that were exposed under the car.
I haven't reset the codes yet because the last time I did I had to reset the vehicle stability control entirely.