Place each salmon fillet on a flat surface. Season both sides with salt, pepper, 1 tablespoon olive oil and lemon juice.
Squeeze excess liquid out of the spinach; discard liquid. In a medium-sized bowl, mix together the spinach, cream cheese, parmesan and garlic. Season with salt and pepper.
Fill salmon pockets with 1-2 tablespoons of the spinach dip, spreading evenly with the back of the spoon.
Heat butter and remaining oil in a skillet (or non-stick pan) over medium-high heat. Add the salmon and fry for 6-7 minutes. Carefully flip and allow to cook on the other side until golden and cooked through (another 6-7 minutes, depending on the size of your fillets).
Optional: cover with a lid and continue cooking for 2-3 minutes, if necessary, until cooked through.
Transfer to a warm plate to make garlic butter.
Melt the butter in the remaining oil/juices in the pan. Add the garlic and lemon juice; sauté until garlic is fragrant (about 30 seconds). Remove and serve with the salmon.