Set a large, 6-quart stockpot or Dutch oven over medium-high heat, and add the peanut oil. Heat the oil to 350 degrees F. Fry the yucca in 2 batches until golden brown and crispy, about 2 minutes. Transfer to a paper towel lined platter and season lightly with salt.

Place a 1-gallon stockpot over high heat and fill with 2 quarts of water. Add the kosher salt and bring to a boil. When boiling, add the lobster tails to the pot and immediately turn off the heat. Let the lobster sit until just cooked through, about 8 to 10 minutes. Remove the lobster from the water and set aside to cool completely.

Once the lobster tails are cool, chop into 1/2-inch pieces and place in a medium non-reactive bowl. Add the lemon, lime and orange juices and stir in the cucumber, red onion and chiles. Refrigerate for 1 hour.

Add the tomato, avocado, chopped cilantro, and olive oil to the lobster mixture and stir to combine. Let sit at room temperature for 30 minutes before serving.

To serve, divide the ceviche between 6 chilled martini glasses, garnish with 3 fried yucca strips and cilantro leaves.