The ornamental design for a buildingedge mount lifting apparatus, as shown and described.
FIG. 1 is a top front perspective view for a building edge mount lifting apparatus showing my new design;
FIG. 2 is a front side view thereof;
FIG. 3 is a back side view thereof;
FIG. 4 is a top side view thereof;
FIG. 5 is a bottom side view thereof;
FIG. 6 is a left side view thereof;
FIG. 7 is a right side view thereof; and,
FIG. 8 is a top rear perspective view.
The screws are shown with a symbolic break in their length. The appearance of any portion of the article between the break lines forms no part of the claimed design.