The easiest way to install a new amp, would be to ensure that your head unit has RCA outputs (phono). Then it is just a case of connecting these to the amp, along with a remote or switched 12v power supply to act as a signal to the amp to tell it when to turn on, and then the amp only requires a 12v feed from the battery and a earth. You used to be able to get small amps like the OEM lexus one, although havent seen them around for a while. so i dont know if you will be able to find one to fit in the original space. As for connecting the the amp up using the loom that was there for the stock amp, it might be possible as all the wires should be there, but if you have removed the original wiring from the amp to the head unit and replaced it with the amp bypass cable, some additional wiring may be required. The other potenital problem is that the power and earth cables supplying the OEM amp may not be man enough for an after market amplifier.
All sounds a little confusing but i hope it helps
Kiff