Heat vegetable oil in a large ovenproof skillet over high heat. Add pork loin and cook 2 to 3 minutes on each side or until browned.
Bake pork loin in skillet, uncovered, at 375° for 10 minutes. Add cider and butter to skillet, basting pork with pan juices. Bake 45 more minutes or until a meat thermometer inserted into thickest portion registers 150°. Cover with foil; let stand 10 minutes or until a thermometer registers 160°. Cut pork into 1/8-inch-thick slices. Reserve drippings in skillet.
Process walnuts and next 6 ingredients in a food processor until smooth, stopping occasionally to scrape down sides.
Spread pesto evenly on 1 side of each bread slice. Layer 6 bread slices, pesto side up, with pork slices, reserved drippings, and lettuce. Top with remaining 6 bread slices, pesto side down.