The ornamental design for a livestockcomb handle, as shown and described.
FIG. 1 is a front elevational view of the livestock comb showing my new design;
FIG. 2 is a perspective view thereof; and,
FIG. 3 is a front view elevational view of a second embodiment of my new design, the only difference being the length of the handle.
The structural features and indicia depicted by broken lines have been provided for the purpose of illustrating portions of the livestock comb handle that form no part of the claimed design.