It's a fairly simple thing you need, check ebay for is200 autoleads amp bypass cable.
The Lexus stereo system (as you've worked out) isn't using standard wiring, where your sony stereo will.
If you get the cable I mention above, it plugs into the cable that leads to the lexus amp behind the glovebox and terminates in a standard iso plug that will fit your sony stereo.
Take out the glove box, unplug the amplifier from the far side, connect that to the bypass lead, which then plugs into your stereo. Simples.