Diagnosis & Repair
WARNING: This page is about a different car, the 2003 Lexus LS 430. However, it is still accessible from the selected car via links, so may be relevant.
Delete DTC and insert all the presently available keys to check whether the engine starts or not. When inserting the key that does not start the engine, note that DTC P0513 will be stored in memory. If all keys start the engine, system is okay. If a specific key does not start the engine, register the key that does not start the engine.