Heat oil in a skillet over medium heat; cook and stir onion and garlic until onion is soft, 5 to 10 minutes. Add liver pate; cook and stir until heated through, about 5 minutes.
Mix apple cider vinegar and brown sugar into pate mixture; cook and stir until sugar is dissolved, 1 to 2 minutes. Add water and bread crumbs; cook and stir until heated through, 2 to 3 minutes. Season with salt and pepper. Remove skillet from heat and cool lechon sauce for 2 to 3 minutes.
Pour sauce into a blender no more than half full. Cover and hold lid down; pulse a few times before leaving on to blend.