Lip product container

The design is the visual features of the LIP PRODUCT CONTAINER shown in the drawings, whether those features are features of one of shape, configuration, ornament or pattern or are a combination of any of these features. The stippled lines are provided for illustrative purposes only and form no part of the subject design. Drawings of the design in seven (7) views are included in which: FIG. 1 is a perspective view of the Lip Product Container in the closed configuration in accordance with the subject design; FIG. 2 is a right side elevation view thereof; FIG. 3 is a left side elevation view thereof; FIG. 4 is a front elevation view thereof; FIG. 5 is a rear elevation view thereof; FIG. 6 is a top plan view thereof; and FIG. 7 is a bottom plan view thereof.