Heat the olive oil in a large pot over medium heat. Add the sliced andouille sausage and cook until the edges brown, about 5 minutes.
Add the diced onion, chopped celery, and minced garlic to the pot. Stir and cook until the onion turns soft, about 4 minutes.
Stir in the rinsed lentils, diced tomatoes, chicken broth, and Cajun seasoning. Bring the mixture to a boil.
Reduce the heat to low, cover the pot, and simmer for 25 minutes until the lentils are tender.
Add the sliced okra and cook uncovered for 8 more minutes. Season with salt and black pepper to taste before serving.