The max recommended is based on them being filled cold. They've accounted for the increased heat that comes with driving the car when they came up with that number.
Thats not true. Max pressure is the highest point at which the tire should operate, not the max you can fill the tire. Anything after that is beyond what the manufacturer can safely say can be in the tire, meaning you are taking risks.
If you're talking about filling time to 45psi at 32 degree weather and then driving them the next day at 90 degree temperature, then you're correct that they would be overinflated. But where does that type of immediate temperature swing occur?
Tires don't just go up a little when they heat up, they go up 5psi or more in pressure. And that can occur after just a couple of corners. Friction creates heat, and tires are where all the weight of your vehicle come into contact with the ground and all that friction, they get VERY hot.
With regular tires, that's probably true. But we're talking about Low Rolling Resistance tires which are harder than the tires that we've used all of our lives. If you look at the max recommended psi on LRR tires, you will see that it's about 10psi higher than what we've all become accustomed to.
Hard tires have existed forever. Low rolling resistance tires are nothing new, they've just become more important now that MPG has become the important factor in new cars.
I had a Civic Hybrid for over 8 years. The LRR tires that the Civic used had a max pressure of 44 psi. I ran them at 40psi the entire time with no issues or uneven wear.
40psi with a car that doesn't weigh that much won't be an issue. I had a set of tires once that If I ran them below 40psi, they would tramline and drive like crap. They were bad tires though and wore poorly on the sides of the tires due to the rather boxy shape of the tire tread.
The next set of tires I got on the same car with the same wheels I would run at ~35psi and they drove just fine. So ideal tire pressure can and does vary on the specific tire, but usually its between 32-40psi on a car that weighs ~3000lbs.
One more thing to consider is that Lexus couldn't make a tire pressure recommendation based on the assumption that people would continue to buy LRR tires with a high maximum psi, They have to assume that many people will buy standard tires when the first set wears out. Therefore, they can't recommend a tire pressure that's higher than is safe for standard tires with a low maximum psi.
Tire pressure recommendations on your door sill are based specifically on the original manufacturer equipped tires, they don't account for other brands of tires or wheels you might install on the car.
I'm fairly certain this is in all the owners manuals, but I do know when I worked at a dealer and asked that specific question that I was told by the manufacture reps that this was the case.