Cowboy,
Congratulations on your purchase, it's a beautiful, high-performing car. I've owned mine for about 18 months, and am enjoying it greatly. I'm guessing that most purchasers are doing absolutely nothing because their cars are on an extended maintenance program. Mine is, and I haven't lifted a finger, but I have some advice for you. But first, answers to your questions:
* Tires cannot be rotated. Like a Corvette or other high performance cars, the tires are unique to the corner that they're on. I have the alignment checked every 5K miles and it has come up needing adjustments 2 out of the four or so times it's been at the dealer. An OOA corner will chew up an expensive tire quickly, and it's not covered by the warranty.
* I'm not changing filters, and doubt anyone else on this list is. I could be wrong about that and would love to hear from someone who IS. I changed my oil at 500 miles and 1,000 miles because I believe that's what you should do for a new car. Get's the metal deposits out of the crankcase. You'll have to pay for the extra changes, but it's totally worth it, IMO.
* I'm brand loyal to Mother's. I use "Instant Detailer" on carbon fiber, and it's awesome.
So, if you read past threads, you might have seen my post about the run flats. They totally suck. They greatly affect handling and acceleration because they are heavy and don't transmit road feedback. And if you get a flat, you're pretty much screwed. You cannot patch them, just replace. I've gotten a flat and it cost me $600. Never again. As soon as these tires are worn out, or as soon as I get another flat, I'll buy "regular" Pilot Sports for it. Who needs a spare when you have Lexus towing service or AAA???
I like to tinker, so I'll likely replace the wheels studs and nuts with titanium items, I'm going to do a benchmark dyno run on it as soon as the pandemic has eased up, and I'll give strong consideration to lighter wheels. Possibly even go down an inch on the wheels to lower the center of gravity.
Use the paddles in the Manual mode, as often as you can. That will keep your shifting chops intact, and it will keep you focused on your revs and your shift points. I'm not that aggressive. When decelerating I downshift at 3,000 RPM, and in most gears, that puts you back to 4,000. When I'm accelerating I use a 5,000 RPM shift point if I'm just goofing around, 6,000 RPM if I'm trying to pass another car in a hurry. I've been on the rev limiter a few times, no harm no foul. First gear is pretty useless.
Last thing, the LC 500 is not a sports car. It's what it claims it is, which is a two seat luxury grand touring car. I traded my Lotus Evora 410 in for my LC 500 because I didn't want to be tempted to race anymore. Been there, done that, no upside, way too much downside. The LC 500 is too heavy to throw around in the twisties. Don't be tempted to try it, because the suspension can't deal with the weight and the steering is vague.
But if you thought that you were getting a gorgeous car that will attract its fair share of attention, which you'll rarely see another one of on the road, which is fast enough to be exciting, and which has Lexus reliability, then you hit the jackpot, my friend. Enjoy!
Doug D.