Head to the West and out the window there. You have a Lieutenant to go chasing after. He will West for a short while and then turn to the North. After that he will turn to the East. Try to catch him before he goes in front of the check point. If he does, take the rooftops and just chase him for a moment. This avoids a very lopsided confrontation. After that he will head to the South and into the Windmill District.
Whenever you catch up to him, you will have to fight him. Use Perfect Parries to quickly subdue him and minimize your own damage. He is a high difficulty enemy. Beat him and the location will be known to Arno.