Pat the salmon fillets dry thoroughly with paper towels, especially the skin, until no moisture remains to ensure maximum crispiness.
Using a sharp knife, score the skin in a crosshatch pattern, about 1/4 inch apart, to help render fat evenly and promote crisping.
Sprinkle the coarse sea salt generously over the skin, pressing it into the scores to help draw out moisture and enhance crunch. Let sit for 10 minutes, then pat the skin dry again to remove excess salt and moisture.
Heat a non-stick or cast iron skillet over medium-high heat until hot and shimmering, about 2 minutes. Add a thin layer of neutral oil and allow it to shimmer and just start to smoke.
Place the salmon fillets skin-side down in the hot oil, pressing gently with a spatula for about 10 seconds to prevent curling. Cook undisturbed for 4-5 minutes, until the skin is golden brown, crackly, and releases easily from the pan.
Carefully flip the fillets using tongs and cook for another 2-3 minutes, until the flesh is opaque and slightly flaky while the skin remains crispy.
Remove the salmon from the pan and let rest for 2 minutes. Squeeze fresh lemon juice over the top for brightness and serve skin-side up to preserve the crispiness.
