I would buy the warranty, but not now. You can buy the Lexus factory extended warranty all the way up until the original 4 year 50k warranty runs out, so take your time and shop around. You can and will find a better deal than that.
I disagree that the things you are trying to protect are the engine and transmission. THOSE are the things I wouldn't worry about protecting.
To me the bigger fear is an electronic failure, the nav screen for instance (Thats a quick $5k.). $2900 won't buy you many Lexus repairs.
I bought the extended warranty on my ES and it paid for itself twofold, and its not nearly as complex as the LS460.
And BTW, everything covered under the factory warranty is covered under the platinum extended warranty, including water pump or timing belt failures.