We report the characterization of the pump absorption and emission dynamic properties of a
$\mathrm{Tm}:{\mathrm{Lu}}_2{\mathrm{O}}_3$ ceramic lasing medium using a three-mirror folded laser cavity. We measured a slope efficiency of 73%, which allowed us to retrieve the cross-relaxation coefficient. The behavior of our system was modeled via a set of macroscopic rate equations in both the quasi continuous wave and the pulsed pumping regime. Numerical solutions were obtained, showing a good agreement with the experimental findings. The numerical solution also yielded a cross-relaxation coefficient in very good agreement with the measured one, showing that the cross-relaxation phenomenon approaches the maximum theoretical efficiency.