Technically, LC uses crumbled cheese. It's not as uniform as diced, but it does offer a lot of surface area for heat absorption.
I've been thinking about this for a long time. The shredded versus sliced versus crumbled versus diced discussion is one of the oldest out there. My biggest concerns (not counting flavor) when it comes to pizza cheese is time, money, consistency, and thermal performance. Not that cheese costs a lot, but it does cost more than any other part of my pizza (dough: $0.55, sauce: $0.48, cheese: $2.12 - for a 14"), so I always have an eye on cost. I hate grating, or even worse crumbling my own cheese because of the time involved, not only in the actual preparation, but also in the greasy cleanup. For consistency I like to buy shredded cheese because I always know it's shredded the same way every time, good or bad. For good thermal characteristics I prefer crumbled cheese. As you can see, I have mixed feelings about this, so I've been working on coming up with a way to satisfy all my concerns. I wasn't prepared to share this with anyone yet because I haven't had a chance to try it out, but the concept is sound, and you're asking the question now, so here it is now:
1) Slice a block of cheese into slices approximately 1/4" using your favorite cheese slicer. (You can go thicker if you like more cheese on your pizza.)
2) Lay all the slices you intend to use on the pizza flat against a cutting board.
3) Take a dough docker and start rolling it over the cheese like you're trying to aerate a lawn. (If you don't own a dough docker you can hammer the cheese with the spiked surface of a meat tenderizer.)
4) Keep rolling until the cheese is almost falling apart, but still held together enough to pick up as slices.
This process offers the following: cheese that takes on a shredded/crumbled openness for better heat distribution, better uniformity of the cheese layer across the whole pizza, low time penalty as the whole process takes under a minute, and low item cost as you can buy blocks of cheese rather than pre-anything.