Heat vinegar in a medium pot over medium heat.
When the pot is hot, add the onion. Sweat the onion for about 5 minutes, until soft and translucent.
Add the garlic and cook for 1 minute, until very fragrant.
Add water/ broth, lentils, and herbes de Provence, then raise the heat and bring the water to a boil. Or precook the lentils to reduce cooking time.
If not pre-cooking the lentils, lower the heat and allow the lentils to simmer until just a tad undercooked, about 30 minutes. Add a bit of hot water to the pot if it gets too dry while simmering.
After the lentils are done, add the mushrooms and cook for about 5 minutes, until tender.
Add the wine to the pot. Raise the heat and bring it to a simmer. Allow it to cook until most of the liquid has cooked off, about 4 minutes.
Stir in the tomatoes, tomato paste, and capers into the pot. Bring it back up to a simmer.
Remove the pot from heat and season the stew with salt and pepper.
Divide into bowls and top with fresh basil. Serve.