Heat oil in 12-inch skillet over medium-high heat until just smoking. Brown sausage well, breaking up large pieces with wooden spoon, about 5 minutes; transfer to slow cooker. Pour off all but 2 tablespoons fat left in skillet.
Add onions, carrots, celery, garlic, and oregano to fat in skillet and cook over medium-high heat until vegetables are softened and lightly browned, 8 to 10 minutes. Stir in flour and cook for 1 minute. Slowly whisk in wine, scraping up any browned bits and smoothing out any lumps; transfer to slow cooker.
Stir broth, lentils, and bay leaves into slow cooker. Cover and cook until lentils are tender, 9 to 11 hours on low or 5 to 7 hours on high.
Gently stir in chard, cover and cook on high until tender, 20 to 30 minutes. Let sauce settle for 5 minutes, then remove fat from surface using large spoon. Discard bay leaves. Season with salt and pepper to taste.