We study the mechanism of the population inversion in mid-infrared fibre lasers based on a chalcogenide glass host doped with active lanthanide ions. Three lanthanide dopant ions are considered: terbium, dysprosium and praseodymium. We predict the relevant trivalent ion level populations and gain. The simulation parameters were obtained by fabricating and optically characterising a series of trivalent ion doped chalcogenide glass samples. We also provide simple analytical expressions that aid the design of the cascade lasing process.