Lexus GS Key Fob Battery Low

Indeed, the symptoms you describe strongly suggest a depleted battery in your key fob. Have you tried replacing the battery yet? What kind of battery does your key fob use? If you have a multimeter, you could also quickly check the voltage of the old battery to confirm it's the culprit.

I haven't tried replacement yet; was confirming the likely cause before doing so. I lack a multimeter. Is there a chance the car itself is failing to recognize the key, or is the battery virtually always the problem?

While it's technically possible there could be an issue with the car's receiver, a failing or dead key fob battery is overwhelmingly the most common cause of these symptoms. Given the age of the battery and the specific errors you're seeing, replacing it is definitely the best first step. Should that fail, a workshop visit would be advisable.

Confirmed: simple battery replacement in the key fob solved it. Cost 37€. Thanks for the confirmation.