Heat a large pot over medium heat with the olive oil. Add the onion, carrot, celery and garlic. Season with salt and pepper. Cook, stirring, until tender, about 4 minutes.
Add the split peas and ham. Stir to combine. Pour the chicken broth, water, bay leaves, thyme and cajun seasoning. Bring soup to a boil. Reduce to a simmer, cover, for 30 minutes.
Add the potatoes. Simmer, uncovered, stirring occasionally, until the potatoes are tender, about 20 minutes.
Remove the bay leaves and thyme stems. Taste and adjust salt and pepper, as desired. Finish with fresh lemon juice and dill, for garnish. Serve and enjoy!