FIG. 1 is a perspective view of the tub cooler with lid; FIG. 2 is a front view of the tub cooler with lid; FIG. 3 is a rear view of the tub cooler with lid; FIG. 4 is a top view of the tub cooler with lid; FIG. 5 is a bottom view of the tub cooler with lid; FIG. 6 is a right side view of the tub cooler with lid; and, FIG. 7 is a left side view of the tub cooler with lid. Broken lines shown in the drawings represent environment only and form no part of the claimed design.