I claim the ornamental design for a locking medicine box, as shown and described.
FIG. 1 is a perspective view of a locking medicine box, showing my new design in a closed configuration;
FIG. 2 is a front elevational view of FIG. 1;
FIG. 3 is a rear elevational view of FIG. 1;
FIG. 4 is a right-side elevational view of FIG. 1;
FIG. 5 is a left-side elevational view of FIG. 1;
FIG. 6 is a top plan view of FIG. 1;
FIG. 7 is a bottom plan view of FIG. 1;
FIG. 8 is a perspective view thereof, illustrated in an open configuration; and,
FIG. 9 is a front elevational view of FIG. 8.
The broken lines showing a medicine cabinet in FIG. 1 depict environmental matter that forms no part of the claimed design. The remaining broken lines in the figures depict portions of the medicine box that form no part of the claimed design.