Lawrence is one of the Joker's goons, usually seen carrying an enormous 80s ghetto blaster that plays Prince (which the Joker seems fond of).
After shooting down the Batwing, the Joker kidnaps reporter Vicki Vale and takes her into the belltower of an old church to await pickup by helicopter. Batman follows them. Upon arriving, he is immediately attacked by one of the Joker's goons, who he quickly defeats. As he strides forward to confront the Joker (who is dancing with Vicki), Lawrence appears above him in the rafters, and prepares to leap down upon the Dark Knight who is unaware of his presence.
With a savage war cry, Lawrence hurls himself down at his enemy with all of his might... and lands a few inches behind Batman, having misjudged his position. His weight combined with the force of the impact causes Lawrence to go right through the floor and fall to his death down the shaft of the belltower.
Batman, for his part, wasn't even aware of Lawrence until he heard the crash. He spins, but Lawrence is already gone, and Batman simply sees a big hole and hears the goon's scream echoing through the church.