Great news! Since your IS came with a 2JZ originally, swapping in a 1JZ is much easier than on other platforms. The bad news is that being a newer vehicle, there are some challenges. Here are some notes from around the internet.
Which 1JZ? – The ideal setup is JZS171 (Toyota crown) as the engine harness/ecu combination is closest to the IS300 as far as ecu and connectors. You want a front sump 1JZ if you plan for it to drop it. Also, prefer to get the VVTi 1JZ which is newer and matches the generation of Lexus. You can use the older non turbo 1JZ in a pinch, but it is older technology..
Cooling – If your 1JZ comes with a hydraulic fan, you will need to convert to a mechanical water pump and pulley. The parts are readily available from Toyota. Your original radiator will work since you had a JZ engine to begin with.
Transmission – Hopefully your IS300 is already 5 speed. So, you just use the same one!
Throttle Cable – Yours will be too short for the 1JZ. Some have used a 1994 Toyota camry throttle cable. Cheap at your local pick and pull yard, or just order from the dealer.
ECU – If you do get the JZS171 1JZ VVTi engine, the harness will mount great in the car. You should go with an standalone EMS, but that is up to you. No need to extend the harness as the ECU is in the engine bay.
Power Steering – The original 2JZGE power steering pump can be modified and fit by the brake booster. Chances are you will not receive a power steering reservoir with your swap engine.
ABS – There will be clearance issues with the ABS block and intercooler piping. You can move it to the side some. One user actually custom made lines to put the ABS block in the battery area, but that is advanced work.