1995 Lexus GS 300 over heating

At what speed did it overheat? If this was at highway speed, the fan isn't even needed thanks to natural air flow. You might consider having your mechanic perform a chemical test at the radiator to check for a leaking cylinder head gasket. That can allow combustion gases to pool under the thermostat which will cause it to not open.

Now that you've added more symptoms, a leaking cylinder head gasket is a good suspect, but there's a quick chemical test that can be performed to confirm that. Typically you'll be losing coolant too. The test involves drawing air from the radiator through a glass cylinder with two chambers partially-filled with a special dark blue liquid. If combustion gases are leaking into the cooling system, the liquid will turn bright yellow. Those gases can pool under the thermostat and prevent it from opening. Thermostats have to be hit with hot liquid to open. Hot air won't do it.

Personally, I'd rather see you spend your money on a head gasket than on a newer car. I am really opposed to all the proliferation of unnecessary, complicated, and expensive computers. As cars get newer, the engineers keep trying to outdo each other to see who can dream up the most insanity.