Won't fresh pasta sheets in lasagna overcook?
Lasagna, using freshly made pasta, can be constructed by (a) pre-boiling the noodles, then building the lasagna, then baking, or (b) layering the lasagna with uncooked noodles, then baking.  Both methods result in a good final product, though you may need a bit more liquid (sauce, for example) in the version that is not pre-cooked.  I've tried both and prefer to cook my noodles first, then bake.  In either case, the noodles do not "over cook".  They should be soft (except perhaps the edges, which I like crispy).  It might seem counter-intuitive, but noodles in lasagna hold up just fine.  By the way, I prefer  most of my fresh pasta cooked longer than 2 - 3 minutes, especially more hearty types, but I get your point.