Recently, a subcellular thin-wire model for the finite-difference time-domain (FDTD) simulation of resistively coated cylinders with lossless insulating and surrounding media was presented. In this paper, it is shown that this model can be extended to lossy cases. The material discontinuity between lossy insulating and surrounding media is corrected as the time-domain boundary condition. The convolution term of the boundary condition is solved by employing a recursive technique. Applying the contour-path integration to the FDTD unit cells around the wire, one may find the coarse-grid-based equation with the correction term and factors for the material discontinuity and the quasi-static field behavior around the wire. In the 2-D cylindrical coordinates with rotational symmetry, the validity of the proposed model is confirmed by an impedance analysis of insulated and resistive antennas according to the electrical properties of insulating and surrounding media, as well as the choice of cell size.