The ornamental design for contact lens case with mirror, as shown and described.
FIG. 1 is a perspective view of a contact lens case with mirror, showing my new design;
FIG. 2 is a top view thereof;
FIG. 3 is a back side view thereof;
FIG. 4 is a front side view thereof; and,
FIG. 5 is a perspective open view thereof.
The broken lines shown in the Drawings for the contact lens case with mirror are for illustrative purposes only and form no part of the claimed design.