The best ways to keep vegetable lasagna from getting soggy are by (1) never using uncooked vegetables as they will release a lot of water during baking, and (2) not using soggy ingredients or ingredients with excess liquid in the lasagna.   Most vegetables contain a high water content. And, if they are not cooked until dry, or strained properly before adding them to the lasagna, then the resulting baked lasagne may be soggy and not set properly.   In addition, if too many vegetables are used in the mixture, the lasagna may be soggy.   Finally, make sure your white sauce gets thick and creamy and is not runny. You just need to cook it long enough for this to happen.