Add the butter, olive oil, garlic, thyme, parsley, lemon zest, sea salt, and pepper into a small bowl. Mash the mixture together with a fork until fully combined.
Place the fish fillets in a baking dish, (I used a 9"x13") and evenly spread the herbed butter mixture over the top. Add 4 slices of lemon on the sides or top of the fish fillets.
Bake until the fish is just done in the center and easily flakes apart with a fork on the edges, 15-20 minutes. An instant read thermometer will read 145ºF.
Serve with the remaining lemon slices.
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Notes
To chop fresh thyme, first remove the leaves from the tough stems, then roughly chop them.