I'm guessing that your ES300 has a theft deterrent system which uses a chip in the key. The system knows which keys are valid and each key has a different chip.
Is the spare a key that was given to you by the dealer? Perhaps that key isn't a chip key?
Programming new keys into the systems usually involves invoking some process while in the vehicle to have the system learn the new keys, and it usually requires a good key to start the programming. The dealer probably has a code or something that they use when there are no valid keys to start the programming. Plus, keys with chips aren't cheap from the dealer. Probably will only involve 1/2 hour of labor, but the keys are the bulk of the price here.
You might be able to find the keys (blanks) at an online parts place for Lexus, maybe try Google. Or, your local hardware or autoparts store may do chip keys now (they do in my area now). Also, some locksmiths have the advanced systems to program new keys, maybe lookup some local ones in your area and at least inquire about your situation.
Maybe claiming the key loss on your car insurance is something to look into?