Honestly, she couldn't put into words why this man put her on edge. Years of soldier instincts, maybe. Lightning knew she couldn't keep watching, not without truly drawing his attention so she purposely doesn't follow his movements.

Instead she simply watched him out of the corner of her eye. Seeing without outright watching. The last thing she wanted was a fight with a fellow 'Hero of Light' on the first day of their arrival. Lightning could handle her gunblade expertly but there were too many innocents around for a confrontation.

So Lightning doesn't engage at all. Let him go on his way and worry about him later. If she could find someone she trusted then she could ask them about him because while he wasn't familiar to her, somehow Light got the feeling that the same wasn't true in reverse.