Jason
Stop driving the car until you get it fixed, water in the transmission fluid will wreck the gearbox and that may cost more to replace than the car is worth!
I have heard of this problem before with the LS430, I was talking to one of the technicians at Lexus Manchester when I was fitting a transmission cooler my 430, he had encountered the the same problem, and it had wrecked the cars gearbox.
The transmission cooling pipe from the gearbox goes through the bottom of the radiator to transfer heat from the gearbox to the water in the radiator. There will be a leak in the pipe inside the radiator allowing water to get into the transmission fluid and transmission fluid to get into the coolant water.
The alternative to replacing the engine radiator is to fit a separate transmission cooler radiator in place of the pipe through the radiator. You then block the ends of the leaking pipe to keep the water in the radiator.
You need to get to a good 'auto transmission' workshop to have the transmission fluid changed asap, I don't think it is a DIY job as you can't get all the fluid out of the transmission by taking the drain plug out. A portion of the fluid remains in the torque converter, this will also be contaminated with water and will need changing.
This is the transmission cooler I fitted to my car: http://www.kenlowe.com/oil-coolers/automatic/index.html
Do not skimp on the quality of the transmission fluid you use, but a good workshop should be able to supply it cheaper than Lexus.
John N