Combine avocados, lemon juice, mayonnaise, and salt together in a bowl; sprinkle in garlic. Mash using a potato masher until dip is creamy.
Heat oil in a deep-fryer or large saucepan to 350 degrees F (175 degrees C). Drizzle about 1 teaspoon oil onto a clean work surface and the bottom of a coffee cup.
Fry the plantains in the hot oil until golden brown, 8 to 10 minutes. Remove from fryer and place on the work surface; flatten with the bottom of the coffee cup. Re-fry until browned and tender, about 5 minutes. Place on a paper towel-covered plate; sprinkle with salt. Serve plantains alongside the dip.