Lexus Troubleshooting Questions? Ask a Lexus Expert
I am sorry that you have not been helped yet. I just came online and saw your question.
Ok, I have uploaded a pdf file with component locations for the immobilizer/alarm/security system for your vehicle. We need to start with checking each on a humid day or after it has rained for any moisture intrusion at those components and then go from there. If you find any in the connectors to the components, dry out and apply some dielectric grease to them and then see if the issue returns or not.
The system is quite complex and does involve quite a bit, which is why it is difficult and time consuming to find the cause of the issue you are having. You start with the components in the engine compartment as they are the ones most affected by humidity or rainy weather.
Sorry, there is no easy answer on this one and is going to require alot of man hours unless you luck out and it is one of the first components checked.