Preheat oven to 400 degrees F.
In a medium bowl, zest lemon; juice one, slice the other, and set both aside. Toss the zest with tomatoes, shallot, and basil. Season with salt and pepper, drizzle with lemon juice, and toss again.
Fold four large rectangles of parchment paper in half, then unfold and lay side-by-side. On one side of each piece of parchment paper, centered about an inch away from the seam, divide lemon slices and arrange in a compact layer. Place fillets on lemon, spread tomato mixture on top, drizzle with 2 tablespoons oil, and season with salt and pepper. Fold paper over along middle seam, then fold and roll edges over ½ inch at a time on all sides, working toward the middle, until the packet is in the shape of a half-moon and about 1 inch of open space remains around fillets.
Transfer packets to baking sheet and bake for 23 minutes. Allow packets to rest before opening, about 3 minutes. Carefully open and enjoy.