In a large mixing bowl, combine drained canned tuna, chopped onion, diced carrot, and sliced green onions. Season with salt and pepper. Add whisked eggs and flour, and mix gently until well incorporated.

Coat hands with flour, scoop small amounts of the mixture, and shape into patties about 2-3 inches in diameter. Aim for uniformity.

Heat oil in a non-stick skillet over medium heat until shimmering. Add patties carefully, making sure not to overcrowd the pan. Cook for 2-3 minutes on each side until golden brown.

In a separate bowl, whisk together mayonnaise, gochujang, fresh lemon juice, and sugar until smooth. Adjust seasoning if desired.

Transfer cooked tuna cakes to a plate lined with paper towels. Serve warm, drizzled or accompanied by spicy mayo.