Ty Gordon, The car possibly is going into limp mode because of misfire, for this reason take care of the misfires first. The P0305 /P0306 code, cylinder 5/6 is misfiring or is randomly misfiring. Maybe check for vacuum leaks as a first step, with engine running(spray starter fluid around the intake manifold base, throttle body, injectors, vacuum lines etc.) and listen for a change in how the engine is running, then check/change the plugs. You could switch the 5 or 6 coils around to different cyl. to see if misfire switches to a different cylinder, telling you coil is probably bad.
Possible causes are: Faulty spark plug cylinder 5/6, Clogged or faulty fuel injector 5/6, Faulty ignition coil 5/6, Fuel injector 5/6 harness is open or shorted, Fuel injector 5/6 circuit poor electrical connection, Ignition coil 5/6 plug/harness is open or shorted,Ignition coil 5/6 circuit plug/poor electrical connection, bad valves, low compression cylinder 5/6, fuel pressure low, Intake air leak,etc,etc. links below give a little more info on misfire codes and how to diagnose. If not comfortable working on your vehicle have a good technician have a look diagnose and estimate repair. Good luck.
I hope this helped you out, if so let me know by pressing the helpful button.
http://www.aa1car.com/library/misfire.htm
http://repairpal.com/OBD-II-Code-P0305
Read more: https://www.engine-codes.com/p0305_lexus.html
http://www.clublexus.com/forums/is-f-2008-2014/835670-help-car-in-limp-mode-po300-p0305-p0306.html