Lexus LS rough idle and stalling

Sounds familiar. I had similar symptoms with my old Saab 9-3. Check engine light, misfires, stalling... turned out to be a defective ignition coil. Have you checked the coil packs, particularly their connections? A loose cable or a corroded plug can cause those issues.

Interesting... I haven't specifically looked at the ignition coils. Where are they located, and is there an easy way to test them without any fancy tools?

On that engine, they're usually right on top of the cylinders, easily accessible once you remove the engine cover. Without special equipment, you could visually inspect for cracks or damage. Otherwise, swap the coil from the cylinder that is reporting the error (via OBD2 reader) with another cylinder and see if the error moves with the coil. Ultimately, without proper diagnosis, I'd recommend taking it to a workshop. A faulty ignition coil can cause long term damage.

I took your advice and had a mechanic check the ignition coils. You were spot on; one of them was defective, most likely caused by a defective connector. Replaced it for 95€ including parts and labor. Runs like new!