In a large Dutch oven, heat 1 tablespoon extra-virgin olive oil over medium heat. Add the carrots, celery and onion. Sauté until they start to soften a bit, about 5 minutes.
Add the sausage and continue to cook, breaking up the sausage as it cooks, until the sausage is nicely browned. Add the lentils and chicken broth. Bring to a simmer and cook according to the instructions on your lentil package. You want to cook your lentils until they are still al dente, just a bit of give, but not mushy.
Add the coconut milk and bring to a simmer. Once it thickens a bit, stir in the kale and let it all simmer away for about 5 minutes.
Serve immediately.