FIG. 1 is a front perspective view showing a first embodiment of a “handle for lid for article of cookware” incorporating the design of my invention; FIG. 2 is a top view thereof; FIG. 3 is a bottom view thereof; FIG. 4 is a side view thereof, FIG. 5 is another side view thereof; FIG. 6 is a front view thereof; and, FIG. 7 is a rear view thereof. The part of the drawings shown in phantom lines depicts the environment of my new design and forms no part of the design of my design.