This will be my first time in Vegas. We are starting in Arizona and touring the Canyonlands and ending in Las Vegas. We will stay two nights at Caesar's Palace.
How early should we arrive at the Las Vegas airport for a 10:15 flight on a Friday in July?
Also, how long does it take to get to the airport from Caesar's??

That would b e a 10:15 AM flight.

8:00. If my experience last January is representative, you should allow at least an hour inside the airport from drop-off at the curb through screening to arriving at your gate. It is a very very busy airport and if your departure gate is in one of the more distant wings, there's a lot of territory to cover.
If you have a rental car to return, add a good 30 minutes for that; the offsite facility operates very smoothly, but it can take 20 minutes on the shuttle if the airport access road is jammed up. Also you might want to leave some time for making a wrong turn and backtracking if you are not familiar with the area.
The airport is very close to the strip, so time from Caesars will depend on traffic. Ask at the hotel for best info.

I did a lot of flying last year and the security check at Mc Carren was the longest wait of them all.

I've even noticed on my tickets that they have special times for Las Vegas and check-in for luggage and boarding. It is always earlier than the rest of the country. So I would get there early.

For its size, McCarren is a very very busy airport. Two hours minimum.

We were leaving on a 6 p.m. flight on a Sunday and the concierge told us to leave the hotel by 3 o'clock -- I was shocked, but they said the airport is so busy on "getaway" days, the security line alone could be more than an hour.

Thanks everyone, I'm traveling with my sister and she always thinks I'm crazy when I want to get to the airport early. Your comments back up my thinking!

If you do get through quickly you'll find lots of slot machines at the gates to pass the time.