I've decided to do a little write-up on how to bypass a factory amp since I haven't seen many around (particularly Lexus ones).

What is needed to start:
Wire strippers
Wire cutters
solder (or butt connectors)
solder iron/gun/torch
electrical tape
basic handheld tools to disassemble various panels/compartments and such of the vehicle
speaker wire (the amount depends on the location of the factory amp. usually between 50-75 ft. will work)
aftermarket headunit
dash kit

What info is needed prior to install:
factory amp location
factory amp OUTPUT wires. inputs aren't going to matter in this situation

BE SURE TO DISCONNECT THE BATTERY COMPLETELY!! POSITIVE AND NEGATIVE TERMINAL!! REMOVE BATTERY FROM VEHICLE!! - This will prevent any problems or complications from any of the steps contained within.

Reconnecting the harnesses after an amp bypass can cause damage to the factory amp, aftermarket radio, and possibly the vehicle. Be sure to follow these instructions carefully.

First, start out by knowing where your factory amp is. (If location is unknown , a good resource is the dealership. Just tell them you are considering replacing it and you want to know the location. Be sure and hint that you may have them install it and/or purchase it from them and they will be more than willing to tell you the location.) Choose which side (depending on amp location) you will run the wires down. Now, remove all panels between the factory radio and the amplifier. If your amp is in the trunk you will need to remove the kick panels, trim panels, the rear seats, and trunk panels on the side of the amp. If your amp is behind the glovebox, you need to remove the glovebox... Be sure to be thorough when removing the panels because this is the part that sets it up to be a great install or a failure. You want to have all of the panels removed to have plenty of access to tuck wires, connect wires, remove and most importantly SEE things!! Don't slack on this part!!

Once all of the panels are removed and there is a clear path from the factory radio location to the amplifier, it's time to get the speaker wire together and mark it for reference purposes. Cut four equal lengths. I usually start out by approximating the first one by setting the speaker roll at the front of the vehicle and walking to the rear. Sometimes there will be little extra taking this route, but it's better to have more than to have less in this situation. If the factory amp is under the seat or behind a glovebox it's easy to just spread it out about the length of the route it needs to travel just to get an idea of how long it needs to be. After getting the length figured out, cut three more pieces of wire that are as close to the same length as the original. Now there are four wires that are the same length. In order to hook everything up properly once the wires are run they must be marked properly. What I usually do is take the first wire and don't mark it at all. Just set it aside. (This will be seen as wire #1 - Front Left speaker channel - more explanation further down) Take the second wire and separate it from the rest. On one side of the wire close to the end, mark it (make sure to use PERMANENT MARKER). I usually make a "stripe" or line perpendicular to the wire so that it appears to be a one. Make sure to do this on both ends of the wire and not only on one. This way it is identifiable at both ends when installed. Now, for the next mark two "stripes" at one end and two at the other. And the last will get three marks at both ends. Double check to make sure the labeling is correct and there will be no confusion. Once that is done, it's time to get the wires organized.

Get all four wires together. It doesn't matter which ends are used. Line them up to be nice and uniform. Grab some tape and with about a 2" strip of tape start taping about 6" from the end that's bunched together and continue down at about a 6-12" increment. The last and first pieces of tape should be about 6" from the ends.

The next step is to figure out which end to start at. I usually start at the factory radio/HU location and feed the speaker wires through the passenger side opening straight down toward the passenger floorboard carpet.
The following will only apply if the amp is in the trunk/under passenger seat: The carpet will need to be pulled up and away from the floorboard to give easy access to the underside (this is why the removal of all the panels was so important.) Once under the carpet continue down the side of the vehicle making sure to pull the carpet up along the way and tuck the wire under as much as possible.
For under the passenger seat location: The seat must be removed completely for the amplifier bypass. Remove seat bolt covers (if present) and remove bolts securing the seat to the vehicle. Be careful when removing the seat as there may be wires connected from the seat to the vehicle that need to be disconnected in order to remove the seat. After removal of the seat, pull the carpet up between the side of the vehicle and the amp and get the speaker wires through and to the harnesses at the amp. Pull all slack through and make sure to not pull too tight!
The rest of the trunk wire run: Continue down the side of the vehicle and run the wires from the side of the vehicle up to the rear seat area. Find a hole (preferably a pre-existing factory location) that the wires can be sent through and send them through. Be sure to make sure that nothing will interfere/hit/damage or otherwise cause problems with the wires or that the wires will not cause problems in re-installing the rear seats properly. Once in the trunk, run the wires down the appropriate side behind all paneling (that should already have been removed) and up to the factory amp location where the amp harnesses already are.

At this point, all of the wires needed are ran and it's time to actually connect these wires. Let's start with the easy part of the connections, the aftermarket wiring harness side. To be clear, the new speaker wires will be directly wired into the aftermarket harness wiring.
Speaker wire connections for reference according to my "marking" method:
wire with no marks - FL (front left)
wire with one mark - FR (front right)
wire with two marks - LR (left rear)
wire with three marks - RR (right rear).
Aftermarket harness connection reference:
FL - white(+) & white/black(-)
FR - gray(+) & gray/black(-)
LR - green(+) & green/black(-)
RR - purple(+) & purple/black(-)
So, with the two aforementioned references, the wires in the factory radio location need to be connected. Choose which side of the wire is going to be positive and stick with it. For example, if the speaker wire has one with a red stripe on it, choose that particular side of each speaker wire to either represent the positive side of the speaker connection. Or, choose the one without the red stripe to represent the positive. It does not make a difference which one represents positive as long as you make a note of it and stick to it throughout all of the connections. This is important to get the right polarity.
Note: Be sure to wire the power connections while making connections behind the radio location. After this process, the aftermarket harness should be completely connected and will not be needed anymore.

Any harnesses currently plugged into the factory amplifier can now be disconnected and do not need to be reconnected except for in very rare circumstances. Reconnecting the harnesses after an amp bypass can cause damage to the factory amp, aftermarket radio, and possibly the vehicle. Be sure to follow these instructions carefully.
Connections at the amplifier will now need to be made. Make sure these connections are to what use to be the outputs of the factory amplifier. The connections will need to be made in the same format that is followed for connecting the harness behind the radio. When bypassing the factory amplifier permanently, the speaker wires that are needed from the factory harnesses may be cut of from the harness and directly wired into the new speaker wires that have been run and connected to the aftermarket harness. If there are plans for possibly using the factory amplifier again just splice into the wires needed while leaving the harnesses unplugged. Using either solder or butt connectors, connect the new speaker wire, according to the reference wiring, to the respective speaker wire lead at the harness. If there are two speakers for the front left channel (i.e. separate door speaker wire and separate dash speaker) that need to be connected to the same channel on the aftermarket radio, connect the two positive wire leads (car side/wires connected to existing speakers in the vehicle) to the new speaker wire positive. Connect the two negatives in the same way. This way all of the front left speakers will be on the correct channel on the aftermarket radio. If one of the speakers in the vehicle is undesired, that speaker may be left out of the connections. Do this for all of the channels/speakers. Be sure to not have any bare wires or loose connections as this can cause problems. Once wired, use electrical tape to clean everything up and replace all paneling in the vehicle in reverse of removal.

Following the procedures above the factory amplifier should be bypassed and all speakers will properly fade/balance from front/rear/left/right. GL and have fun!!