I think the lasagna layers won't break down nearly as fast if they don't have the sun on them, that's probably why it's recommend it for sunny gardens. For shade, you might want to buy some compost (or make your own) and then work it into the soil instead, same effect in the end just a little more work for you.
I did a lasagna garden sort of thing on my "mailman path", which is mostly in the shade, and it worked great. I did buy a bunch of compost to mix in with it, though, to help it "cook" faster. That was a couple of years ago and right now I really need to get out and weed it! :-)