Pull the puff pastry from the freezer and set it out to thaw for 30 minutes.
Heat the olive oil over medium heat in a large skillet. Add the onions and garlic and sauté until the onions are translucent, about 5 minutes. Add the celery, carrots, and mushrooms and sauté for an additional 5 minutes.
Once the carrots and celery are tender, add the lentils, vegetable broth, tomato paste, liquid smoke, vegan Worcheshire sauce, soy sauce, and spices. Bring to a boil and then reduce heat to simmer. Cover and simmer for about 30 minutes until all the liquid has evaporated and the lentils are cooked all the way through. Remove from heat and stir in the pecans and ground oats. Taste and adjust seasonings.
Preheat the oven to 400F. Once the puff pastry has thawed, transfer it to a floured surface, and gently open it fully. Scoop the lentil mixture into the middle of the puff pastry, packing it tightly into a log shape. Leave about ½ inch on the top and bottom to seal up the sides. Pull one side of the puff pastry over the lentil mixture. Cover with the other side, pulling enough that it overlaps the first half by 1 inch. Pinch it together. Fold the top and bottom up and pinch it together.
Transfer the loaf to a parchment lined baking sheet, seam side down. Score the wellington by making diagonal cuts about 1 inch apart. Turn and cut it the other way diagonally so that you have diamond shapes on your loaf. Brush with non-dairy milk or olive oil and bake for 30-35 minutes, until the Wellington is golden brown.
Let the Wellington cool slightly before gently cutting into slices with a serrated knife.