Sprinkle 1 1/2 tbsp. salt over both sides of salmon. Place salmon on a platter and let cure in the fridge for 1 hour.
Preheat oven to 250°. Place the salmon in a dutch oven or pan just large enough to contain it (you don’t want excess room in the pot, or you’ll be wasting precious oil). Pour 2 cups oil into the pot, making sure to cover at least three-quarters of the fish. Place bay leaves, thyme, oregano, and lemon slices in the oil. Cook salmon until the fish has turned a bright orange color and the flesh has firmed up and flakes easily, 25 to 35 minutes. Allow salmon to cool in the infused oil, ideally overnight, in the fridge. Transfer salmon and oil to an airtight container.
When ready to eat at your campsite, in a large skillet over medium heat, add 2 tbsp. of infused oil from the salmon preparation. Fry the eggs until almost cooked. Gently place pieces of salmon in between the yolks to warm as the eggs finish cooking. Remove from heat and garnish with fresh basil. In a large bowl, combine radicchio and frisée, add salt and oil to taste and toss to combine. Divide lettuces among plates, top with eggs and salmon, and serve.