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I noticed your fuel gauge is on empty. More than likely your 3 pumps sucked up some dirt from the bottom of the tank and is clogging one or more of your injectors. Remember injectors atomize the fuel in a very fine mist having dirt blocking the injector will result in engine performance issues.
Also running your tank to empty multiple times will result in one of your pumps failing due to the in tank pump over heating. i have seen this happen first hand with poorer people running their cars to the bottom of the tank because they cant afford to keep fuel above a quarter of a tank.
Your driving one of lexus flagship cars of their time. If you cant keep fuel above a quarter of a tank, i suggest you buy something you can afford to keep fuel in. No pun intended, not trying disrespect you, Im just saying maintaining these cars is pretty pricey.
If your Hybrid battery goes out can you afford to replace it?
Have an OBD2 code reader hooked up to see what the car computer says in depth. Many auto parts stores can do this for free. The fuel filter should protect injectors from tank debris but anything is possible. Sometimes we drive too gently and you just need to put your foot into the pedal on the highway. Put some fuel system or injector cleaner in the gas tank. These ideas won't damage your car and are inexpensive to do as a first step. Hard to guess if 135000 miles is enough to require professional cleaning/replacement.
Also running your tank to empty multiple times will result in one of your pumps failing due to the in tank pump over heating. i have seen this happen first hand with poorer people running their cars to the bottom of the tank because they cant afford to keep fuel above a quarter of a tank. /QUOTE]
Good point. Fuel is needed to keep the fuel pump(s) on cars from getting over heated and burning up. Running on empty is not a good idea. I keep my LS's fuel level at a minimum of 1/4 quarter tank. It's just not worth the risk.
oh and while you are at it go find where the vent for the battery is.... likely near the rear shelf or trunk its needs to be cleaned. if its not too dirty now damaged might be avoided... this is one thing that most people don't check... venting/cooling for the hybrid battery. And go buy some liqui molly injector cleaner/fuel system and run it through with some gas and see if that helps.