Installed engine and trans mounts in my 2002 LS430, some notes from the install:
My car drove smoothly to begin with, however, there was a leaking oil pan, oil dipstick and oil level sensor O rings. Pan bolt on front were sitting very close to subframe cross member when compared to photos of other cars, so decision was made to replace the mounts when raising engine to remove and reseal the oil pan. Oil dipstick and oil level sensor O rings are only accessible when driver side engine mount is removed.
If you are replacing the oil level sensor O ring, plan on a re-pin of the sensor connector (plug).

Part numbers:
engine mounts: 12361-50170 need 2
trans mount: 12371-50140
oil level sensor O ring: 90430-27001
oil dipstick O ring: 96721-19010
oil sensor connector (plug): 90980-11235

Work was completed on a car lift, doing the mounts on ramps or jack stands is not impossible, but it would be very difficult.
Removing the two bolts that hold the oil and trans dipsticks together and to the block is the most difficult part of the job. There is almost no side access to the bolt that holds the assembly to the block. A Milwaukee 14mm deep set socket that have flat sides and using a 14mm wrench on that flat sided socket was the only way break the mounting bolt loose. The angles are really, really difficult. Replacing the 14mm bolt that bolts the trans and oil dipstick together is a two man job, it is extremely difficult. There is no space to put the bolt in place and then turn bolt to get it started.

Procedure: Many youtube videos showing how replace the engine mounts and removing the oil pan to reseal, search for them to give you an idea. The method used was as follows (using a car lift, not jack stands or car ramps):

Use an under hood engine lift as shown on many youtube videos, remove engine cover, loosen power steering reservoir, heater control valve from firewall, loosen air box lid from airbox.
DRAIN ENGINE OIL AND REMOVE OIL FILTER.
Loosen lower engine mounts bolts, place engine bay hoist in engine bay, to make job far, far easier, place piece of wood under oil pan and use an under engine jack to push the engine up, then tightened the engine bay lift to hold engine in place. With the engine now supported by the engine bay lift above the engine, remove the jack you used to push engine upwards via the oil pan. Engine is supported in a high enough position to give access to oil pan bolts.
Remove all engine oil pan bolts, remove oil pan, clean up engine and oil pan mating surfaces. Place Toyota black FIPG (or whatever sealant you find as your favorite) on the oil pan, put oil pan back in place, torque oil pan bolts.
I would suggest allowing the sealant cure fully before putting engine oil back in oil pan, I waited overnight.

Turning attention to motor mounts: both front wheels were removed, passenger side engine mount is easier, remove ground wire and 4 block upper engine mount bolts. You very well may have to push engine up higher, use the under car engine jack to lift engine higher in order to make the mount bolts clear subframe (which is why I allowed the oil pan sealant to cure overnight).
Driver's side engine mount: remove four mount bolts from block, unplug oil level sensor to create additional space, manipulate engine mount and remove. Steering column will be in your way. In the case of this car it was fortunate that the engine mount was separated on the car which created more space for removal.
While replacing driver side mount remove the four 10mm oil level sensor bolts, pull sensor out and replace O ring. My car had a completely hardened O ring that broke apart in pieces.
To remove oil dipstick, loosen the two 14mm bolts that hold the dipstick tube in place (this can be quite difficult), pull dipstick tube up and cut off hardened O ring. DO NOT REMOVE DIPSTICK TUBE ANY HIGHER THAN NECESSARY TO REPLACE HARDENED O RING.
Put the driver side mount back in place and loosely bolt the four mount bolts to the block.
The most difficult part of the job: getting the two 14mm bolts that hold the oil and trans dipsticks together and the mount for the dipstick bolted back onto the block. There is no easy way to do this. You will have to find what works for you.

Lower engine from the above engine lift onto the engine mounts, tighten all the bolts to torque, replace the oil filter and engine oil before restarting engine.
After replacing the engine/trans mounts bottom edge of oil pan now sits 30mm above the cross member.
The car now drives amazingly smooth!

 

Hi "JIM" (OP).

I wish to thank you for this writeup post! It was very helpful. ESPECIALLY, your mentioning of the oil level sensor O Ring! AND providing a Lexus part number. With that knowledge, I ordered (from Bell Lexus, AX.) the mounts, and O Ring. My old one was brittle and leaking! Mikeceli