Slice lemons as thinly as possible; remove seeds. Toss slices with 2 cups sugar; transfer mixture to a flat resealable plastic container. Place in the refrigerator overnight.
Place butter, salt, remaining 3/4 cup sugar, and flour in the bowl of a food processor. Process until mixture is crumbly and starts to hold together.
Heat oven to 400 degrees. Line a 12-by-17-inch baking pan with parchment paper. Press dough evenly into the bottom and up the sides of the pan, making sure there are no holes. There should be at least 1/2-inch crust of dough going up the sides of the pan. Bake until golden brown, about 20 minutes. Transfer to a wire rack to cool completely, about 15 minutes
Place lemon-sugar mixture and eggs in the bowl of a food processor. Process until lemon rinds are in 1/4- to 1/2-inch pieces, 30 to 40 seconds. Pour mixture over cookie crust. Bake until set, 15 to 20 minutes. Cool on a wire rack. Trim 1/2 inch around edges of pan. Cut into about sixty 1 1/4-by-2-inch pieces. Sift confectioners' sugar over cookies.