Heat the olive oil in a large pot over medium heat. Add the onion, bell pepper, and celery. Cook for 5 minutes until the vegetables soften.
Stir in the garlic and Cajun seasoning. Cook for 1 minute until fragrant.
Pour in the diced tomatoes with their juice and the vegetable broth. Add the salt and black pepper. Bring the mixture to a simmer.
Add the sliced okra. Simmer uncovered for 10 minutes, stirring occasionally, until the okra begins to soften.
Gently place the cod pieces into the pot. Simmer for 6 to 8 minutes until the fish turns opaque and flakes easily.
Remove the pot from the heat. Ladle the stew into bowls and top with chopped parsley. Serve with lemon wedges on the side.