Preheat oven to 400° F.
Heat the olive oil and butter in a large skillet over medium heat. Once hot, add the mushrooms, onion, and garlic to the pan. Cook, stirring frequently, until the mushrooms have released their moisture and the onions are translucent.
Add in the thyme leaves and flour. Mix the flour into the butter then pour in the vegetable broth and almond milk. Bring to a boil until thickened.
Add in the mixed vegetables, potato, and lentils. Season with salt and pepper
Pour the mixture into a deep pie dish or casserole dish and set aside.
Ina large bowl, mix together the flour, salt, butter, and ice water until a dough forms. Being careful not to overwork, place the dough between two sheets of parchment paper or a silicone baking sheet and roll out to the width of the pie plate. Carefully transfer the crust to the plate, crimping the edges down. Make a few slits in the top for air to escape.
Transfer to the oven and bake for 45 minutes or until the top is golden brown. Serve immediately.