Is it true that putting spices in something then baking it destroys the spices?
It is not true that baking destroys spices (for most spices I know; unless you put them to bake dry on top of something, which might burn them).

I made this answer a bit broader as we add flavor to food not only with spices but with herbs or flavorful vegetables, mushrooms, and fruits as well.

Baking/heat will likely change the texture and flavor of spices, vegetables, and especially fresh herbs, but it will not destroy them. Sometimes it will take away the fresh sharpness (like in garlic or onion).

Sometimes frying or roasting spices before cooking is even desired to give them a slight toasty flavor (like whole cumin and other spices in Indian cuisine). Some say that "only with roasting all flavors can be unlocked".

So it depends on what effect you want to achieve with a spice/seasoning.

And in your case putting spices into lasagna before baking will help blend the flavors together. However, putting some fresh herbs on top of the lasagna before serving will give the dish some color and freshness.