Buy a few spare brake light bulbs and a spare brake light switch. These are common failures. I had my switch fail on my out west trip. 15 minutes in a parking lot. Back up and running.
Check the rear driveshaft. Carrier bearing do tend to die. Would rather deal with that a month in advance than on the road.
If your coolant bleeder "T connector" is original, either go ahead and replace it or throw a spare in the back.
X2 on micro start jump box and ID tool. The ID tool saved us on our trip out west.
Check and recharge your AC. I think this will be obvious but it gets HOT AS CRAP driving out there. Also swap your cabin and vehicle air filters. Cheap insurance as it can get dusty AF out there. I did bring a spare engine air filter, but didn't need it.
Sunscreen. This is for real. Get the spray stuff and throw it in the back. Also on the highway, I wear one of those Columbia Fishing shirts. You just sit there, baking in the sun. Covering your arms will save you great discomfort. The sunscreen is for when you are on trail with the windows down. Re-apply every 3 hours. Or not. You do you.
Throw in a bottle of windex/window cleaner. The bugs on I-70/I-40 are for real. Also convenient to have a cleaner in the car. The 2nd row door cup holder holds a windex bottle quite nicely. Also I recommend new wiper blades and topping up with RainX windshield wiper juice. It'll make life easier. FYI, wiper blades off of Rock auto are STUPID cheap. Just get 2 sets and I typically destroy a set on an out west trip.
Get 3x rolls of quarters for car washes. We had super bad mud build up in the wheels and had to pull over twice to blast it all out. Having quarters in the console made life easy. Also throw in a roll of gorilla tape and a roll of painters tape. Just in case. Sometimes plastic bits work themselves loose. Slapping a bit of tape that won't murder your paint will make life easier. Also throw on two coats of wax on the car before going. This will help get junk off of the car afterwards and protect it. Or not. Whatever.
For my out west trip last year, when we stopped for fuel, I did a full check under the hood. This year, I just did it once a day. Once a day checking everything provides a good piece of mind.
Buy these books:
https://funtreks.com/
I have Moab and Colorado. They basically bring so much win, I cannot begin to describe it. They have Cali, etc. WORTH IT. I know Gaia is great, etc but these books in front of you make all the difference.
Get ALL of the fast USB chargers. We were always charging a phone, radio, lantern, whatever. If you can standardize cords or at least USB charging devices, it makes life that much easier. My ham radio couldn't charge off USB, but we barely used it so it was fine.
Speaking of Electronics, if you don't have bluetooth in your LR3, buy one of these:
https://www.amazon.com/Kinivo-BTC480-Hands-Free-Multi-Point-Connectivity/dp/B06Y2D1ZX8
I've had mine for a year and a half and my friend has the previous version for a few years. The cords are long enough to reach the rear AUX port and 12v charger. WORTH IT if music off your phone is important to you. It is VERY important to me, so however that works out for you. Super easy to swap connections to another phone, etc. Sound quality is great for the aux port and hands free actually works pretty good.
Ouray/Telluride/Silverton, I would do on the return trip. They still have CRAP TONS of snow. Last week, the snow drifts were still 20ft tall. So I doubt the trails will be open/passable. But by the end of July, you might have a bit more luck. Try to do AS MUCH AS POSSIBLE. Also if you are staying in Ouray, and camping, cut the crap and camp at the Ouray KOA. Its super nice there. Also shower house ******. Also all the restaurants in Ouray are pretty mediocre (please note I live in ATL, our food here is premium, so I'm a bit spoiled). Either way, the food there will be overpriced, ok-ish, and vastly inconvenient. Before arriving in Ouray, get all the food beforehand and try to cook/prepare on your own. It'll be A TON easier and quicker. Also if you can hit the trails by 8-9am local time, YOU ARE GOLDEN. Everyone else is still waiting at the one breakfast place to get a table while you are shifting into low range. After lunch, the trails can get crowded, but it is what it is. The trail heads get crowded around 11am or so. But you'll be ~2 hours on down the trail by the time the tourists show up.
In Colorado, when descending trails covered in loose rocks, like shale, USE HILL DESCENT CONTROL. It makes life a ton easier. But otherwise, I was in low range, rock mode, HDC off, either in Drive, or manual mode. Usually in manual mode, cruising in 2nd gear or whatever was needed.
Costco or Sams club card will save you BIG $$$. Sams club if you drive in I-40, Costco is on I-70. However that works out for you. On I-70, there is legit a Costco every 300 miles or so...right there in your range. My LR3 was getting 16-17 mpg out there and back. For my Colorado trip, I did not pack a spare fuel can. I did in Moab, and we did use our spare fuel. However we picked extremely long off road routes. In Ouray, just gas up before hitting the trails. Saves you a lot of headache. Spare fuel is such a hassle, avoid if you don't need to. For Colorado, you don't need it. Fuel in Ouray is expensive but easier than spilling 5 gallons on my boots. Also down by Silverton on US550, there is a decent Shell station.
Its weird, I'm used to driving junk, but this LR3 has been a champion for cross country trips. They are extremely comfortable and pretty darn reliable.
For driving out there and back, I recommend 2 drivers per vehicle, at least. Swap out as needed. For the first day, I try to do at least 15 hours of driving then crash at a hotel. After 15 hours, everyone is pretty toast. Driving back, allow extra time due to time zone changes. Also if you can avoid traversing Denver and I-70 in Colorado, that'll save you many headaches. Both obstacles are miserable. At least check google maps/waze for updates but typically on I-70 west of Denver, the interstate is blocked by
____ (insert today's vehicle ruining everything) and holding up traffic. I-40 was far more relaxing but I don't know your route, so however that works for you.
As mentioned before, you do you, but these are the details I've found to make it a bit easier. I've done two cross country trips with my LR3 and its been a pretty darn awesome vehicle for the job.
Anyway, there ya go. Enjoy.