OK, the hitch is installed. The hitch itself took an hour, accessing the electrical plug-in took two hours. How Lexus can charge $400+ for just the install labor is beyond me. This was the first time for me and it took extra time to assemble the correct tools and scratch my head a few times. It could probably be done in 2/3 of the time for someone experienced.
Tools necessary for installing the hitch to the frame:
14 mm socket
15 mm socket
6" socket extension
air impact wrench makes it easier, a regular 1/2 socket wrench would do and is definitely necessary for 4 bolts.
torque wrench to handle 37 ft-lbs or torque could be guessed
Tools for the rear floor removal:
a panel removal tool or something that will remove black plastic body clips (plugs), a small stiff putty knife works fine.
12 mm deep and shallow socket (a magnetic insert is HIGHLY recommended)
6" socket extension
3/8" in socket wrench (a 3/8" air socket wrench speeds things up)
The hitch/frame install is straight forward. After removing the tow hooks, there is a brace to install on the driver's side and one for the passenger's side - 4 bolts total. The mounting holes on the car are plugged with rubber grommets. Removing them exposes the welded and threaded backing nuts. The holes line up perfectly and just wrench the remaining 9 bolts through the hitch and into the frame or brace. There is also a 15mm nut. I jacked up the rear to gain better access and used a jack stand to steady one end of the hitch while the other was secured by one barely started bolt to hold it in place. Then the other end got a bolt and the rest was easy. Then the wiring harness can be untaped and clipped on to little mounting brackets on the hitch. Pull the obvious large rubber body grommet and the grommet on the wiring harness goes in its place. The grommet is flexible and is easily installed. The easy part is done.
The interior rear floor removal is necessary. There are no shortcuts. All of this needs to be done just to remove the little tray on the driver's side to gain access to the electrical plug in. "Front" is front of the car, "rear" is rear of the car. The tray with the jack in it comes out with the removal of two black plastic body clips on the rear part of the tray. The tray lifts up and to the rear and that is it for that one. The jack door is left on and the contents of the jack tray can be left as they are.
The hinges for the rearmost two tray access doors are held on by four nuts that are exposed when the jack tray is removed. A 12 mm deep socket is needed for those front four nuts. Then the rear of the hinges are held on by six 12 mm bolts that are hard to access and the rear tray has to be flexed a bit to get to them. Don't worry at this point if one is dropped - it will be found when the tray is removed. There are some more black clips on both sides of the tray and then it can be lifted out.
A couple of more clips allow the very rear panel that has the tray opening buttons in it to be pulled up. It is secured with several non-accessible white clips that can't be seen but comes out easily.
Finally the small tray on the driver's side that is really why all the rest of the floor has to be taken out can be removed. It is held in place by a couple of black clips and a strange threaded plastic nut in a depression on the bottom of the tray. Don't forget to un-Velcro the interior gas door release.
There is only one place to plug in the wiring harness and the length of the wire from the grommet makes it obvious. Taping the hitch wire to the body harness is advised so you don't have to do this twice in case it comes loose somehow. Of course, test the trailer plug-in now to make sure it works. Lights, LT, RT, brake, and emergency lights. Some of this testing is redundant but it pays to do it anyway.
Re-installation is the reverse of removal.
EXCEPT: Don't forget to get the gas door release out from behind the little final tray when it is put back in.
AND: The six 12 mm bolts for the rear tray's doors are a real pain. Access is limited, they are hard to start in their holes, and dropping one can cause it to roll under the rear tray and then the tray has to be removed again to get the bolt. Luckily, I had a magnetic socket insert than held the bolt so it could be started by hand. Some wide masking tape can be used to close the three gaps where the bolts might fall through. Another trick might be to put the bolts through the hinge first and then lower the door/hinge to just above the holes and use the 12 mm socket w/extension to get them started. Just start all six bolts first in case one is dropped under the tray. Then they can all be tightened after they are all started.
Hope this helps someone. Pictures were considered but they would not have been any more help than the drawings that came with the hitch installation instructions.