Lip product container

The design is the visual features of the LIP PRODUCT CONTAINER WITH LIP PRODUCT 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 eight (8) views are included in which: FIG. 1 is a perspective view of the Lip Product Container with Lip Product in the open configuration in accordance with the subject design; FIG. 2 is a right side elevation view of the Lip Product Container with Lip Product; FIG. 3 is a left side elevation view of the Lip Product Container with Lip Product; FIG. 4 is a front elevation view of the Lip Product Container with Lip Product; FIG. 5 is a rear elevation view of the Lip Product Container with Lip Product; FIG. 6 is a top plan view of the Lip Product Container with Lip Product; FIG. 7 is a bottom plan view of the Lip Product Container with Lip Product; and FIG. 8 is a perspective view of the Lip Product Container with Lip Product in the closed configuration.