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curious that some chefs don't say to cover. I always thought that covering helped it cook through more quickly and evenly - keeping in the steam and heat so that the insides of the dense dish cook. Especially if you're like me and don't precook noodles! then taking the top off for the last 15 or 20 minutes get you the crisp top. I have never cooked a lasagne completely uncovered - wonder what happens!
I can assure you that in Italy they don't cover lasagne to cook. But then, it's not filled with a wet, sloppy sauce al' americano either. Crispy edges are actually a good thing as is restraint on the saucing. The pasta "leaves" aren't in there just for bulk, they are the star of the show.
I believe that some lasagnes may be assembled "higher/taller" so covering would assist with the dish's overall cook through. My simple home-made basic cheese & pasta is short, so i cover for half the cooking time in the beginning. My meat/cheese/and veggie one is so tall & massive, requires my all-clad lasagne pan, and is covered for 90% of the cooking time. Also, I know my crappy stove and its inconsistent oven settings.
For recipes where pre-baked pasta is used (is that what it's called? -- the kind that cooks through in the oven), extra liquid is added and the pan is covered to let the pasta sheets cook through. This is a special situation. Even though you can find this kind of pasta imported from Italy, it is not the classic situation. Maybe that's what's at work in the recipes you've found.
I know that I've never covered lasagne while it bakes. However, susan g is correct. My mom uses those pre-baked pasta noodles for lasagne sometimes and she has to cover it for it to cook through, even though she still finishes it uncovered and sometimes under the broiler to get it crispy on top. Personally, I like it best uncovered and thoroughly crisped all over.
I only use the "no boil" noodles when making lasagne in a camp Dutch oven & pour red wine around the sides to help steam them. So, using boiled pasta & sauce & meat that are already cooked I don't really see the need for covering the lasagna. Just baked one uncovered & loved it -- cooked fairly quickly, didn't need time to set up & wasn't runny. Also no cheese sticking to the foil!!!