It would appear to be either an ECU or wiring problem as IGT is generated by the ECU to trigger the coil.I've copied some info from Iatn which may be of interest,from this it seems your Lexus will run without IGF(but with MIL on) so it's a bit different to the older systems I'm used to.

Appendix D
Continued

Technical Reference & Specifications
__________________________

DIAGNOSTIC REFERENCE INFORMATION


Ignition Circuit (IGT & IGF Signals)

Circuit
Description
The ignition timing (IGT) and ignition fail (IGF) signals provide crucial
information in the control of ignition system timing, injection timing,
and Fail-Safe activation. Based on an initial timing angle calculated
from the NE and G signals, the ECM outputs an IGT signal to the
igniter as a reference point from which it determines ignition dwell
period. A special circuit inside the igniter controls the ignition dwell
period by controlling when the power transistor is switched on. When
the ECM determines the proper time to provide spark, it turns the IGT
signal off, which turns the igniter power transistor off, producing a
spark.

The IGF signal is used by the ECM to determine if the ignition system is
working and to protect the catalytic converter. When the ECM does not
detect the IGF signal, the ECM goes into fail-safe mode. With no IGF
signal, the ECM will store a DTC(s), depending on model year and
number of cylinders affected. There are different fail-safe modes
depending on the ignition system, cylinder displacement and model
year. The following is general summary.

IGT & IGF Signal Relationship



The IGT signal triggers the igniter power transistor. Without IGT,
spark will not occur. The IGF signal confirms that an ignition event
has occurred. Without IGF, the ECM shuts down injection pules.




General Summary
If there is no IGF signal on engines before 1998 model year, the ECM will
enter fail-safe and turn off all the fuel injectors.

Beginning with the 1998 model year, V-6 and V-8 engines equipped with
direct ignition system with integrated ignition coil/igniter (1 ignition
coil/lighter per cylinder), the engine will still run without the IGF signal,
but the MIL will be on.

Beginning with the 2001 model year on 1 ignition coil/igniter per cylinder
engines, the ECM fail-safe will turn off the fuel injector if there is no IGF
signal for that cylinder and if engine conditions (such as load and
temperature) are sufficient to damage the catalytic converter. If the IGF
signal returns to normal while the engine is running, the injector may
remain off until the next engine start.

Due to the rapid, high frequency nature of these signals, inspection
should be performed using an oscilloscope or high quality digital
multimeter with frequency capabilities.





Troubleshooting
Hints


• On older systems, if engine will not start due to missing IGF, injectors
will pulse once or twice during cranking. Use injector test light to
confirm this condition.

• Scan data indicates an injection duration even when injectors are
disabled due to IGF fuel cut fail-safe.

• Regardless of the type of IGF fail-safe mode, the IGF DTCs must be
diagnosed before attempting to diagnose a fuel system/injection (P1305 is an IGF DTC)
problem. The IGF DTCs are one trip DTCs.

• Use oscilloscope to diagnose IGT and IGF circuits.