The unit is that of a velocity. If you have bins of equal $\Delta \ln \lambda$, then each of your pixels (in your spectrum and in the template) represents a constant velocity increment $\Delta v = c |\Delta \ln \lambda|$, which could have units of km/s.

The shift in the peak of a cross-correlation function is known as "the lag" and the velocity shift is given by the lag (in pixels) multiplied by $\Delta v$.