Position racks in the upper and lower thirds of the oven and preheat to 350 degrees . Line 2 cookie sheets with parchment paper. Using an electric mixer, beat the egg whites with 1/8 teaspoon salt at medium-high speed until stiff peaks form, about 3 minutes. Gradually mix in 1 1/2 cups confectioners' sugar and beat until thick and glossy, about 2 minutes. Fold in the peanut butter until just blended.
Using a 1-inch ice cream scoop, place 16 mounds of the cookie mixture evenly on each prepared cookie sheet. Bake, switching and rotating the sheets halfway, until golden, 20 to 25 minutes. Let cool slightly on the sheets, then, using a metal spatula, transfer to a rack to cool completely.
Meanwhile, using an electric mixer, beat the butter with the remaining 1 1/2 cups confectioners' sugar and 1/8 teaspoon salt on medium speed until fluffy, about 5 minutes. With the mixer on low speed, beat in the banana and lemon juice.
Spread the banana frosting on the cooled cookies and sprinkle the peanuts on top.