Slow isn't the goal - just remember that. Collection and balance is the goal.
Get up and jog around your room at a natural, steady pace. Imagine that is the canter of a hunter horse. Forward moving, ground covering, and doesn't take an extended amount of energy to travel long distances (which is why people jog and not run for exercise). Now, jog some more, but imagine jogging in slow motion. You have to support your weight on your one leg, slightly bent, all while keeping good posture etc. This is what you're going to ask your horse to do. Going slow is HARD, it take muscle and tires them out much more that going at a nice easy pace. This is of course, if you're going to as them to lope correctly and not just trop around. So, you can't expect your horse to lope slow right off the bat, they have to develop the muscle and they have to be willing to do it - because after all, if you're going to show western - you'll more than likely have to have drape in your reins if you want to pin. So going slow can't be an uncomfortable or regretted thing for your horse - he should enjoy it to an extent and be comfortable preforming it.
Compare these two lopes:
(will start loping at approx 1:40)
The first lope is choppy and quick and the horse doesn't look like he's happy at all. His body is stiff in every way and he's not supporting himself on the hind end. If you watch his inside hind leg, what the hock and how far it drives under his body - not far at all. This shows that he shallow in his hind end and thus not rocked back and lifting the front end. Because he's heavy in the front, he must compensate and quickly "pedal" his forlegs to catch himself. If I was working with this horse and rider, personally I would put the horse in a smooth snaffle and simply get the horse's natural cadence and suspension back back asking him to preform that nice, "easy" canter (like you jogging around the room) and get that swing back in his hip (and thus, he must release the tension in his back) and allow the front end to lighten naturally and give him the ability to stretch his shoulders and get that "sweeping" front leg we light to see. That would be the building blocks to a good lope - you have to go 'fast' to go slow.
Now, appreciate the second video. This horse is obviously a good mover, but beyond that you can see that he WANTS to go the pace he's at and that's because his trainers have set him up physically to be able to preform it with ease. Watch the tempo of his legs, they are much "slower" than compared with the previous video and swing easily and the horse can sweep across the arena. This is a good lope - the lope you should strive for.
Now, to start - does your horse move at all gaits with a relaxed back? If no - then there's no point and going any further. You should be able to walk, trot, and canter with only soft feel of his mouth and he should travel at a consistent, relaxed pace. His natural pace. Until he is consistent under saddle at his natural, comfortable pace, you're never going to be able to make his comfortable at an unnatural pace. If he is relaxed, start adding lateral work to build up back muscle and make him lift his abdomen and then at the walk and jog ask him to start moving his shoulders/hip independently. This all will set him up to lope quietly and relaxed.