I have owned my IS300 for almost a year now ('01, Automatic with roughly 230k miles) and it has recently started making a very interesting clunking noise when I take off from a stop. This noise occurs ONLY when I have been driving the car for around 20-30 minutes and everything is hot and up to operating temperature. Basically, when release my foot from the brake and allow the car to slowly move forward it will result in multiple (quite loud and destructive sounding) rear clunking/popping noises, sometimes coming from what seems to be the right side, sometimes the left side and sometimes both. When this happens the car simultaneously lurches, similarly to if someone had let a small amount of slack from a rope. Another problem that could potentially be related is that when I am at highway speeds and I release my foot from the accelerator I begin to feel a very subtle vibration.

I originally thought it could be a differential backlash problem, so I swapped the standard open diff to an M98 LSD, along with S9 solid diff bushings, yet I am still experiencing the noise. My only thought could be either a bad U-joint, bad axles or maybe a bad trans mount – any suggestions would be greatly appreciated.

 

Could be axles. I experienced something similar to you but in a different car and it was the axles.
Do the sounds happen when the car shifts gears? Because my IS300 with Xcessive mounts has a hard 1-2 shift on the auto that happens if the car is in gear and coasting down hill . No only is it rough to feel, almost like a jerking motion, but its a loud sound also. In my case I know its a sound made by the transmission.

 

When was the last time you did the brakes? Pads, rotors, shoes. What you're hearing could be a dragging brake problem