Efficient and power-scalable laser operation of a vibronic Tm3+:KLu(WO4)2 microchip laser at ∼2.13 μm is demonstrated. In the continuous-wave mode under diode pumping at ∼805 nm, this laser generated 1.17 W at 2109–2133 nm with a slope efficiency of 39%. This emission is related to the coupling of the electronic transitions of Tm3+ ions with the stretching vibrations of the WOW oxygen bonds in the monoclinic KLu(WO4)2 crystal host appearing at ∼379, 406, and 450 cm−1. The achieved emission wavelength is longer, to our knowledge, than any previously reported laser based on Tm3+ or Ho3+ doped double tungstate crystals. Passive Q-switching of the vibronic Tm3+:KLu(WO4)2 laser is realized with a single-walled carbon nanotube (SWCNT) based saturable absorber, representing the longest wavelength in this mode of operation. In this regime, the maximum output power reached 0.70 W at 2131 nm, corresponding to a slope efficiency of 29%. The pulse characteristics were 25 ns/1.1 μJ at the pulse repetition frequency of 0.62 MHz. These are, we believe, the shortest pulses ever achieved in any lanthanide-based laser passively Q-switched by carbon nanostructures. A conventional (purely electronic transition) Tm3+:KLu(WO4)2 microchip laser at 1.92 μm Q-switched by the same SWCNTs generated 40 ns/4.0 μJ pulses corresponding to a peak power of 0.1 kW, which is a record value for this type of laser oscillator, to our knowledge.