Make the aioli: Combine the mayonnaise, lemon zest and juice, mustard and garlic in a food processor and process until combined. Transfer to a bowl, cover and refrigerate 1 hour before serving.
Meanwhile, prepare the mushrooms: In a shallow pan, soak the mushroom strips in the buttermilk, about 1 hour.
Make the batter: In a large bowl, combine the egg yolks, beer, flour, cornmeal, 1 teaspoon kosher salt, 1/2 teaspoon black pepper and the cayenne. Fill a large deep pot with about 1 1/2 inches peanut oil; heat over medium-high heat until a deep-fry thermometer registers 350 degrees F.
In a large bowl, beat the egg whites with a mixer until stiff peaks form. Gently fold the beaten egg whites into the batter. One at a time, dip the mushroom strips in the batter, then carefully lower into the hot oil. (Do this in batches if necessary-do not crowd the pot.) Fry until golden brown, 2 to 3 minutes, turning with tongs. Remove and drain on a paper towel-lined plate. Sprinkle with sea salt and serve with the garlic aioli.