FIG. 1 is a right front perspective view of the ornamental design for a first embodiment laundry storage device according to the invention;

FIG. 2 is a front elevational view of the laundry storage device of FIG. 1;

FIG. 3 is a right side elevational view of the laundry storage device of FIG. 1, the left side of which is a mirror image thereof; and,

FIG. 4 is a top plan view of the laundry storage device of FIG. 1.