Preheat a 4-quart soup pot over medium-high heat. Sauté the onion in the oil with a pinch of salt until translucent, about 3 minutes. Add the garlic and sauté for about 15 seconds, then stir in the thyme and paprika.
Add the lentils, broth, salt, and a few grinds of black pepper. Cover and bring to a boil. Once boiling, lower the heat to medium and cook for 25 minutes, stirring occasionally, until the lentils are almost tender.
Add the tomatoes, crushing them with your hands as you add them. Bring back to a boil, then lower the heat and simmer for another 20 minutes or so, until the lentils are very tender.
Add the spinach and olives and stir until the spinach is wilted. Add a splash of water to thin if needed. Taste for salt — the olives are salty so hold off on adding more until after they go in. Let sit for 10 minutes or so for the flavors to settle, then serve.