You do mean is300 don't you?
The other remote (the spare) is the battery good in it and did you try it several times?
Thanks
Are you located in Europe? It appears to be a european model Lexus.
You Dealer (maybe local repair shop) should have a tester like this....
http://www.keyfobtester.com/
This will test the signal and how strong/weak the signal is. It would take all of 1-2 minutes to test and they shouldn't charge you but it will let us know if the remotes are the problem. And it will help us by not replacing parts that are good.
If they both test good then the problem lies in the keyless entry/security ECU. These computers have been known to go bad and it a simple replacement and program your old remotes to it. I'm not sure how much the ECU would be but I'd ask while you're there having the keyfob's tested.
Please click accept if I have been helpful. Thanks, Genchi
Technician
Toyota Certified Master Diagnostic Technician, ASE Master Technician with L1 Advanced Engine
Sorry no info no good
read a link on lexus owners club and reprogrammed the key fob and now working