Cut twelve 12-inch squares of aluminum foil or parchment paper.
Set a square on the work surface so one corner points toward you.
Below the imaginary midline that divides the square into two triangles, place a slice of tomato and a small amount of shallot; top with a piece of fish, a portion of the olives and capers, some salt and pepper, and a pinch of thyme.
Sprinkle with 1 teaspoon lemon juice and a few drops of oil.
Fold the triangle top down over the fish.
Seal the packages by firmly folding over the edges three times and place the package in a large baking dish.
Repeat with the remaining squares and ingredients.
Bake for 15 minutes, rotating the pan in the oven after 10 minutes to ensure even cooking.
Carefully open one package; the fish should be opaque in the center.
If it is not, reseal the package and bake the fish about 5 minutes longer.
Serve 2 packages per person, allowing each diner to open his or her own at the table.