A Balrog Run is to go to a predefined area of interest to search for an unkown person or object. This phrase was originally coined by the youtube channel, worldoftheorange.
Ex. 1
Me: "Harry Potter sure does have a shitty time finding horcruxes."
Friend: "Yeah. The last three movies are just one big balrog run."
Ex. 2
Person 1: "I saw this really hot girl walking between classes the other day. I haven't seen her since though."
Person 2: "Then I guess its time for you to go on a balrog run."