Sounds like your ECU may have a leaky capacitor. Fairly common on Toyota/Lexus of this era. Even if this isn't the root cause of this issue I would stress checking it and having it repaired if any are leaking.
Aside from that, i'd check for vacuum leaks (spray brake clean over hoses and everything air would pass through to get into the engine), test your MAF for good measure and just give the engine bay a thorough once over, look for any loose or damaged wires, basically any dumb shit that usually happens on older stuff.
MAF test for 2JZGE
http://my.prostreetonline.com/2014/09/18/how-to-test-a-2jzge-maf/