I am making a roasted vegetable lasagna, refrigerating uncooked overnight and baking the next day. Will this result in a flatter lasagna?

No, you'll be fine!

Are you using veggies for the noodles? I have no experience with that but I do regularly make lasagna and either freeze it or put in in the fridge to be cooked the next day and have never had any issues. I also do not use the no cook noodles, I use regular noodles and then assemble the lasagna with the noodles uncooked and they cook while baking the lasagna.