Heat the olive oil in a large pot over medium heat. Add the sausage and cook until browned, breaking it up with a spoon as it cooks.
Add the diced onion and cook for 3 to 4 minutes until it softens. Stir in the minced garlic and cook for 1 minute more.
Pour in the rinsed lentils, diced tomatoes with their juice, chicken broth, and oregano. Bring the mixture to a boil.
Reduce the heat to low, cover the pot, and simmer for 25 minutes until the lentils are tender.
Stir in the chopped kale and cook for 5 minutes until it wilts. Season with salt and black pepper to taste before serving.