Rinse fish cold, dab dry and cut into large pieces. Mix 3 tablespoons lemon oil, basil and a little pepper. Place the fish in a bowl and sprinkle with the marinade. Cover and chill for about 1 hour.
In the meantime, peel the cucumber for the salad and cut or slice it into thin slices. Quarter the melon and scrape out the seeds with a spoon. Peel melon and cut into bite-sized pieces. Wash, clean and halve strawberries, quarter larger fruits.
Wash the herbs, shake dry and chop the leaves.
Whisk honey, vinegar, salt and pepper. Fold in 3 tablespoons of lemon oil. Mix cucumber, melon, strawberries and herbs carefully with the vinaigrette. Let the salad steep for about 30 minutes.
Heat a pan. Fry the fish for 2-3 minutes on each side. Brush with the marinade and season with salt. Arrange the fillet pieces with the strawberry-cucumber salad.