In a small bowl mix together the smoked paprika, lemon pepper and salt. Rub liberally over the pork tenderloin and reserve.
In a large cast iron skillet over medium-high heat, add the oil. Sear the pork tenderloin on all sides until evenly browned. Transfer to a pan sheet lined with a rack. Put into the oven and cook the tenderloin for 10 to 15 minutes.
Remove from the oven to a cutting board and allow to rest. Once rested, slice the pork into 1/2-inch rounds. To assemble sandwiches, lather aioli on both sides of the dinner rolls. Divide the pork, bacon, lettuce and spicy pickles among the rolls, transfer to a serving platter and serve.
In a small bowl, whisk all the ingredients together. Warp and place in refrigerator until ready to serve.