Preheat oven to 350 degrees F. Cut chicken into cubes and cook with salt and pepper to taste. In a bowl, mix cooked chicken with onion, cilantro, taco seasoning and lime juice.
Fry corn tortillas in olive oil in a fry pan or you can also use a deep fryer with canola oil. They only need to fry for 3-5 seconds (until they float to the top). Pat them dry as they come out of the oil.
Fill the tortillas with 1/4 cup of the chicken mixture and roll up like a burrito (don't have to tuck the ends in if you don't want to). Place rolled tortillas into a 13 X 9 inch baking pan. Heat two cans of soup, 1 can of milk, and pepper jack cheese until all cheese is melted and ingredients are nicely combined. Pour cheese mixture over tortillas. Put shredded cheddar cheese on top.