Clean the mushrooms. Remove the stems from the shiitakes, then slice the caps very thinly. Slice the oyster mushrooms very thinly as well.
Coat the bottom of a large pot with 4 tablespoons of the oil and place it over medium heat. Give the oil a minute to heat up, then add the mushrooms. Cook them for about 10 minutes, stirring occasionally, until they're very tender and a bit browned around the edges. Remove the mushrooms from the pot and transfer them to a plate.
Add the remaining tablespoon of oil to the pot. Once the oil is hot, add the onion. Cook the onion for about 8 minutes, stirring occasionally, until it softens and just begins to brown.
Add the garlic, ginger, cinnamon stick, cloves, cardamom pods, star anise, cumin seeds, fennel seeds, and peppercorns. Stir for about 30 seconds until fragrant, then add the paprika, cumin, and turmeric, followed by the flour. Cook the mixture for about 1 minute more, stirring constantly, until it becomes very fragrant.
Stir in the tomato paste. Cook everything about a minute longer, stirring constantly.
Slowly add the broth while stirring, then add the lentils and return the mushrooms to the pot. Raise the heat and bring the liquid to a boil, then lower the heat and let it simmer for 40 to 50 minutes, until the lentils are very soft and beginning to break down, and the stew is thick. You can add more broth or some water if it gets too thick at any point.
Remove the pot from heat and stir in the lemon juice. Season the stew with salt to taste, if desired.
Ladle into bowls and serve with your choice of toppings.