In a large saucepan with a lid, heat oil over medium-high. Add onion and cook, stirring, until softened and browned, 3 to 5 minutes. Add tomato paste, oregano, and thyme; stir to combine.
Add lentils, 5 cups water, and tomatoes with their juice; bring to a boil. Reduce heat and simmer, partially covered, 20 minutes. Add chard stalks and cook until beginning to soften, about 5 minutes. Add chard leaves; season with salt and pepper, and cook until lentils and chard are tender, 15 to 20 minutes.
Stir in lemon juice; ladle soup into bowls. Drizzle with olive oil, and serve with bread, if desired.