Heat the olive oil in a large pot over medium heat. When the olive oil is hot, but not smoking, add the onions, carrots and celery. Cook the vegetables for 5 minutes, stirring frequently.
Add the garlic to the pot and cook for 1 minute, stirring almost constantly.
Add the andouille sausage to the pot and cook for 2-3 minutes, stirring frequently.
Add the lentils and chicken broth. Stir to combine the ingredients well, while gently scraping any bits off the bottom of the pot.
Raise the heat to high, when the broth comes to a boil, lower the heat to medium-low and cover the pot.
Cook the lentils for 30-45 minutes, until they reach the desired tenderness.
Taste the lentils and add salt if needed. As a reference, we did not add extra salt to our lentils.
Serve the lentils with rice or a generous piece of bread.