I have 138,000 miles on my 2000 Lexus ES 300 (Platinum Series), do I have to replace the Timing belt even though I don't see any leaks at all in front or around the engine?

It depends on how many miles have passed since the timing belt was last changed. If no maintenance history, change the timing belt, water pump, and thermostat immediately, if not sooner. While the front of the motor is apart, that is the time to change the water pump, since it is right there in the open. No use paying to change the belt, then later paying another labor charge to change the water pump. Do everything at the same time. If the belt is within the scheduled change intervals, and the water pump is leaking, have the pump and thermostat (it's not too much money) changed. Do you see any leaks? Leaking coolant could be a water pump, or a loose hose, among other things. If oil is leaking, it could be a front main seal, loose oil filter or residule oil from the last oil change, loose drain plug (have I got a story to tell about one of those), or, as what happened to my '96 ES300, a valve cover gasket decided to take a permanent vacation. The Lexus is not an inexpensive car to maintain, but with proper care and feeding, you will enjoy it for many years. Thank you.