The object of the present article is a one-dimensional lattice-gas model of soft particles, wherein particles interact only if they occupy the same or a neighboring site. The model is intended as a simple representation of penetrable particles of soft condensed matter. To represent different scenarios, two different realizations of the lattice model are considered: a one-component and a two-component system. For the two-component case particles of the same species repel and those of opposite species attract each other. The systems are analyzed entirely within the transfer matrix framework. Special attention is paid to the criterion devised in Ref. [Phys. Rev. E 63, 031206 (2001), 10.1103/PhysRevE.63.031206], which serves to separate two types of behavior encountered in one-component penetrable particle systems. In addition to confirm the existence of a similar criterion in the one-component lattice-gas model, we find that the same criterion can be used in the two-component system for predicting the occurrence of thermodynamic catastrophe.