Heat the coconut oil in a large, high-walled sauce pan or dutch oven over medium-high heat. Add the onion and pepper and sauté until tender, about 4-5 minutes.
Add the garlic and ginger and saute until fragrant, about 30 seconds.
Add the sweet potatoes, seafood stock, lemongrass, cilantro, and lime zest. Bring to a simmer, cover, and cook until the potatoes are just tender, about 10-12 minutes.
Pour in the coconut milk and lime juice and return the pot to a gentle simmer. Season the cod filets with salt and pepper, then nestle them in the liquid so they are fully submerged. Cover and cook until the cod is opaque and flakes easily, about 5-7 minutes.
Remove the cod and sweet potatoes with a slotted spoon and divided into shallow bowls. Season the broth with salt and pepper to taste, then ladle it into the bowls. Garnish with fresh cilantro and lime wedges.