I'm not sure exactly how your fuel tank and pump are designed, but it if is the pump-submerged-in-tank system, that could also explain at least part of it. With that system, gasoline flowing through the tank helps keep the pump lubed...if you run the tank dry (or the level of fuel in the tank gets below the tank's intake-port), the pump is electrically-operated and, in some cases, keeps running for awhile, sucking nothing but air, which can damage or degrade the pump, lessening its performance even when the tank is filled up again. I'm not saying that's exactly what happened to your car, but it has been known to happen in similar circumstances. That's why some Owners' Manuals caution against letting the tank go dry....though, obviously, if the gauge failed, that's not your fault. Still, it's a good idea to fill up based on mileage, not just a gauge-reading, which could be off. Fill the tank every 150-200 miles or so, and you generally won't run it dry, no matter what the gauge reads.
Also, if my memory was correct (I once had an IS300 with the same 3.0L in-line 6) that engine was designed for 93 octane.