Peel and roughly chop the potatoes. Cover with water in a medium pot and boil until tender, about 15 minutes.
Drain and mash the potatoes. Add the sardines and mash again. Stir in the onion, salt, dill, flour, garlic, lemon zest, egg and breadcrumbs until well combined. Use your hands to shape the mixture into six cakes.
Heat a large skillet over medium high heat. Add the olive oil and when hot, arrange as many cakes in the pan as you can without crowding. Sauté the fish cakes until golden brown and crispy, about four minutes per side. Repeat with the remaining cakes, adding more oil to the pan as needed.
Drizzle the lemon juice over top and serve one to two cakes per person with some fresh greens.