Quasi-continuous-wave laser operation of 20 at.% Tm:LiYF4 thin films (84-240 μm) grown by Liquid Phase Epitaxy (LPE) on undoped LiYF4 substrates is achieved. The 240 μm-thick Tm:LiYF4 active layer pumped at 793 nm with a simple double-pass scheme generated 152 mW (average power) at 1.91 μm with a slope efficiency of 34.4% with respect to the absorbed pump power. A model of highly-doped Tm:LiYF4 lasers accounting for cross-relaxation, energy-transfer upconversion and energy migration is developed showing good agreement with the experiment. The pump quantum efficiency for Tm3+ ions is discussed and the energy-transfer parameters are derived. These results show that LPE-grown Tm:LiYF4 thin films are promising for ~1.9 μm thin-disk lasers.