The ornamental design for a wall-mounted hanging lantern, as shown and described.
FIG. 1 is a front, top perspective view of a wall-mounted hanging lantern showing my new design;
FIG. 2 is a rear, bottom perspective view thereof;
FIG. 3 is a front elevation view thereof;
FIG. 4 is a rear elevation view thereof;
FIG. 5 is a left side elevation view thereof;
FIG. 6 is a right side elevation view thereof;
FIG. 7 is a top plan view thereof; and,
FIG. 8 is a bottom plan view thereof.
The broken lines shown in the figures are for the purpose of illustrating portions of the wall-mounted hanging lantern that forms no part of the claimed design.