Sounds like a fuel or spark issue. How many miles on the vehicle? Any maintenance history on repairs? Can you confirm that either are working correctly? Before it wouldn't start, did it run rough on acceration suggesting the fuel filter is plugged? Also, there may be some fuses to check for ignition. Lastly you may be able to check error codes if you can purchase or borrow a scan device.
x2. If the starter turns over strong but it won't start, fuel isn't getting to the cylinders or it's not igniting. I find it hard that none of the 8 cylinders would ignite. Maybe some issue w/ the fuel pump or could be a dirty mass air sensor (do you run a K&N type filter?).
I'm having starting issues lately as well. 2003 LX470 92000 miles. The battery is fully charged and when I turn the key it cranks and cranks strong until it times out maybe 5 seconds or so. I turn the key agin and it fires right up. Acceleration is strong and smooth across the board.
I've changed the fuel filter and was about to inspect the condition of the pre filter around the fuel pump.
Any thoughts? Oh, by the way I live in Panama, as in Republica de Panama... So fuel quality might be suspect.