The ornamental design for a lawn mower grass catcher bag with zipper side-opening, as shown and described.
FIG. 1 is a perspective view of a lawn mower grass catcher bag with zipper side-opening, showing my new design from the front, top, and right side, the left side being a mirror image thereof with the zipper side-opening omitted;
FIG. 2 is a front elevation view thereof;
FIG. 3 is a rear elevation view thereof; and,
FIG. 4 is a right side elevation view thereof, the left side being a mirror image thereof with the zipper side-opening omitted.