Do you eat eggs?
I dice mushrooms and add them to my veggie burgers quite often (I do use a black bean base- but I imagine lentils would work in place- maybe partially pureed/mashed). The burgers do hold better with an egg/egg white but there are other options like flax or maybe chia seeds that would help them bind.
I would cook up your veggies and mix with mashed lentils and quinoa/brown rice. Bind with something (maybe add some breadcrumbs as well).
Here's my recipe! recipes.sparkpeople.com/recipe-detail.asp?