In a large bowl, combine lime juice, olive oil, hot sauce, salt and pepper and mix well. Toss in tuna, avocados, cilantro, onion and pickles and fold into the sauce.
Cover and refrigerate while you prepare the tostadas.
In a heavy bottomed frying pan, heat the vegetable oil over medium high heat. When the oil is hot, add in 3-4 tortillas (or however many fit in your pan with some space to breathe). Fry on each side for 2-3 minutes or until crisp and golden brown.
When tortillas are done, move them onto paper towels and sprinkle with salt. Top with the tuna salad, additional cilantro and a squeeze of lime juice.