'01 IS300 won't start - security problem

have an '01 IS300 that occasionally will refuse to start. starter cranks forever but no turnover so we are immobilized out for 2 hours or more. The security light flashes entire time so it is not recognizing the key. Have 2 keys and both behave the same. Both work or both fail. Typically has happened when car is hot. Have tried disconnecting the battery and making sure contacts are clean and tight. Sometimes seems like that has helped (car has started) but may just be coincidence. Seems like a loose connection or failing component somehow. In the first shop for 2 days, hard failed but shop not equipped to diagnose. Towed to 2nd shop but not failing. No codes thrown from all the attempts to start that sent us to the first shop but (after starting engine at 2nd shop) when 2nd shop tried a different key with incorrect code, it did throw a code that incorrect key was detected. Sounds like when it is failing, security system doesn't even know a key is present. What is most likey failure here?

have an '01 IS300 that occasionally will refuse to start. starter cranks forever but no turnover so we are immobilized out for 2 hours or more. The security light flashes entire time so it is not recognizing the key. Have 2 keys and both behave the same. Both work or both fail. Typically has happened when car is hot. Have tried disconnecting the battery and making sure contacts are clean and tight. Sometimes seems like that has helped (car has started) but may just be coincidence. Seems like a loose connection or failing component somehow. In the first shop for 2 days, hard failed but shop not equipped to diagnose. Towed to 2nd shop but not failing. No codes thrown from all the attempts to start that sent us to the first shop but (after starting engine at 2nd shop) when 2nd shop tried a different key with incorrect code, it did throw a code that incorrect key was detected. Sounds like when it is failing, security system doesn't even know a key is present. What is most likey failure here?
well although it was not a lexes i had a very similar problem that contained the same symptoms exact same way turned out to be the little security brain box a fellow mechanic friend of mine found it by mistake it felt real hot to him and he placed a damp cold rag on it to cool down and after a few minuets it would start dumb me had to test his theory about 5 times but after replacing it never had that problem seems heat would cause a break down some where in that thing