Lexus ES Cold Start Issues

That definitely sounds like a fuel delivery issue. The poor running and hard starting, especially when cold, points to that. Have you had the injectors tested? A faulty cold start injector could absolutely cause those symptoms. I experienced something similar with my old Mazda years ago. Rough idling until it warmed up. Turned out to be a clogged injector. You might want to look into getting a fuel pressure test done as well. If the pressure is low, then that will tell you there's a fault somewhere in your fuel supply.

Thank you for the prompt response! I haven't had the injectors specifically tested, no. I was hoping it would be something simpler. How involved is an injector test, and is it something I can do myself with basic tools? Also, if it is a faulty injector, is replacement the only option, or can they sometimes be cleaned or repaired? I'm trying to get my head around the best course of action before heading to the workshop.

The injector test itself isn't too difficult if you have the right tools, but getting to the injectors on some cars can be a real pain. You'll need a fuel pressure tester and some way to actuate the injectors, plus the knowledge of what the correct pressure and spray pattern should be. Unless you're very confident, I'd suggest taking it to a trustworthy workshop. Cleaning them is an option, but it's not always successful, especially if the valve is defective. Given the symptoms you're describing and the age of the car, a defective injector seems a likely culprit. Looks like you might need to brace yourself for visiting the workshop.

I appreciate the insights and experienced advice. It does indeed sound like a job best left to the professionals. I took the car to my local mechanic. Following the injector tests, it turns out the cold start injector was indeed defective, costing me 515€ for the repair. Happy to report that the car now starts perfectly and runs smoothly, even on the coldest mornings. Many thanks!