Could a Lyon-class battleship reasonably fight a Francesco Caracciolo-class battleship?
Short answerThe comparison favours Caracciolo in a duel because its speed lets it choose the engagement, while Lyon's sixteen-gun battery becomes more dangerous if other forces can slow the Italian ship.
NotesThe comparison gives Lyon sixteen 13.4-inch guns and a speed of 21 knots, against Caracciolo's eight 15-inch guns and 28 knots. That seven-knot advantage would let the Italian ship choose range, angle and timing. Caracciolo's turret armour is quoted at 15.7 inches against Lyon's 11.8 inches, while the belts differ only slightly at 11.9 and 11.8 inches. Deck protection complicates a simple claim of superior armour: the figures given are two inches for Caracciolo and 1.7 to 2.8 inches for Lyon. The Italian guns are also credited with roughly one kilometre more effective range. In a fleet battle, French carrier aircraft or other forces that slowed Caracciolo could allow Lyon's much larger number of shells to matter. A duel gives the faster ship more freedom, including opportunities to engage from a bearing on which only part of Lyon's battery can reply.