In this paper, we discuss theoretically the effects of lossy chiral material on guided electromagnetic waves in parallel-plate waveguides. The guided-wave structures filled with chiral materials have been named chirowaveguides, and their guiding properties for lossless chiral materials have been recently studied and reported in the literature. Here, we extend the analysis of chirowaveguides to the case of lossy chiral materials, and we theoretically investigate the effect of material loss on guided modes in parallel-plate chirowaveguides. Dispersion diagrams for the real and imaginary parts of wave numbers of guided modes along with their electric and magnetic field components are given and the similarities and differences of these quantities with those of the lossless chirowaveguides are addressed. These guided-wave structures can have potential applications in the design of novel devices and components, and in electromagnetic shielding. The associated theoretical analyses for lossy chirowaveguides are steps toward further understanding of wave interaction with lossy chiral materials in wave guiding structures, and can be stepping stones towards the design of novel measurement techniques for determining material parameters of lossy chiral composites.