IMO lutzes, even learning singles, need two things, more than other (toe) jumps:
1) Speed and commitment into it. Going into jumps too slow never works well, but with a lutz it's especially important to go blazing into it, or you can't get enough power to convert and fully do the counter rotation. This is scary when you first start to learn even the single. I would imagine that it's at least 3x as scary when going for the triple.
2) Getting the toe pick in exactly the right spot, relative to the skating foot on the back outside edge. This needs to be emphasized when learning the single and then again learning the double. Too many coaches let students get away with placing the toe to the outside of the skating foot arc, which pulls you over to the inside edge = flutz. Flips and toe loops are slightly more forgiving, in that if you're a couple of inches off with toe placement, you can still manage a decent jump.