Pat the tilapia fillets completely dry with a paper towel to ensure a perfect, golden sear.
In a small bowl, combine the Cajun seasoning, sea salt, and black pepper.
Rub both sides of the tilapia with 1 tablespoon of olive oil, then sprinkle the spice mixture evenly over the fish.
Heat a large cast-iron or non-stick skillet over medium-high heat until very hot.
Place the tilapia in the pan and sear for 3-4 minutes per side until the fish is opaque and flakes easily with a fork, then remove from the pan and set aside.
In the same skillet, add the remaining 0.5 tablespoon of olive oil and the trimmed green beans.
Sauté the green beans for 5-6 minutes, adding the minced garlic during the last minute of cooking, until they are bright green and slightly blistered.
Squeeze fresh lemon juice over the fish and beans just before serving for a bright, acidic pop.