The ornamental design for a lightingsystem for a tow truck, as shown and described.
FIG. 1 is a perspective view of a lighting system for a tow truck showing my new design;
FIG. 2 is a front elevational view thereof;
FIG. 3 is a rear elevational view thereof;
FIG. 4 is a right side elevational view with the left side being a mirror image thereof;
FIG. 5 is a top view thereof; and,
FIG. 6 is a bottom view thereof.
The broken line showing of alpha and/or numeric indicia on the lighting system is for illustrative purposes only and forms no part of the claimed design.