Heat oil in a soup pot over medium heat. Brown kielbasa coins for 5 to 6 minutes, turning once, then transfer to a plate.
Cook onion in the same pot for 5 minutes, scraping up browned bits. Stir in garlic for 30 seconds, then add lentils, broth and bay leaf.
Bring to a simmer, cover partly and cook for 15 minutes. Add squash and browned kielbasa and simmer for 15 to 20 minutes more until lentils and squash are tender.
Stir in kale and pepper and simmer for 6 to 8 minutes until the leaves are tender. Remove bay leaf, stir in vinegar and divide among 6 bowls.