The isothermal layer is the layer in any medium at where all points have the same temperature. Thus, by definition, the lapse rate of temperature in an isothermal atmosphere is zero.
Source:Hardy, Colin C., Ottmar, Roger D., Peterson, Janice L., Core, John E., and Seamon, Paula. 2001. Smoke Management Guide for Prescribed and Wildland Fire 2001 Edition. Produced by the National Wildfire coordinating Group Fire Use Working Team.