How to tell if my IS300 has LSD?
Look at the sticker on your driver door sill/jamb, look for the area that reads "A/TM"
You'll see numbers such as B02A, B02B, B02C
B,C = LSD
If you are still unsure, call 1800 25 LEXUS and ask them to look up your VIN and they can tell you what options it came equipped it from the factory.
If you bought your car second hand, there is a possibility the owner of a non-LSD IS300 swapped in a factory LSD, if this is not disclosed, it makes things a bit more challenging.
Here are pics and info on how to distinguish the two by looking at the gears; http://my.is/forums/showthread.php?p=3637468#post3637468
The methods of doing a burn out and checking if there are one or two tire marks / jacking up the car and spinning the wheels are somewhat debated and I am unsure if this is a valid way of determining if your car has lsd or not.