I was just watching a video of the FEI Endurance Championships, and the horses (who were STUNNING, by the way!) cantered most of the way. Do you ask for a specific lead when you're on an endurance ride, and do you have to switch every so often to make sure one side isn't weaker?
First, you are mostly going to be trotting. There are three reasons you see most people looping in those video:
1) They're FEI and it's a lot more competitive than AERC. I, and most people in my area, tend to avoid the few FEI rides in our area because there tend to be more people who are in it for the competition and that comes with less support, camaraderie, and more people who are willing to put their horse's well-being at risk in order to win. Granted, there are those in AERC that do that as well, but it's more often found in FEI.
2) They're very experienced. I highly encourage you to begin with LSD (Long, Slow, Distance) as that is the only way to truly build up your horse for endurance. If you choose, you can add speed later, but for now, you should focus on simply finishing.
3) These are videos - they're going to show off horses at the most exciting 5 miles o so - the part you don't usually see are the 45-95 miles where they're just plodding along and it doesn't make for very good video haha. Horses and riders perform differently when they know eyes are on them - just as every horse with its head up and ears forward for every endurance picture going "OMGOMGOMG - Monster in the bushes with a giant, clicking mouth that's going to EATME!!"
Now, to answer your question, yes, when you lope, you do want to switch leads every now and then so that you strengthen/wear out the horse evenly. Same goes for posting - you need to switch which leg you're posting on every now and then. You might be surprised at how easily they train us to get comfortable posting on the same leg all the time when we're not paying attention!