By employing double-walled carbon nanotubes as a saturable absorber to start mode locking, we experimentally demonstrate dual-wavelength operation of a passively Q-switched, mode-locked (QML) Tm∶LuAG bulk laser at the wavelengths of 2017 nm and 2027 nm. Herein, the laser is pumped by a wavelength-tunable Ti∶sapphire solid-state laser, and when the absorbed pump power is greater than 2292 mW, the laser enters a stable QML state of operation. By using an output coupler with transmittance of 3%, when the absorbed pump power reaches 6.7 W, the QML output power is 1.28 W, corresponding to a slope efficiency of 22.39%. The repetition rate is 102 MHz, which corresponds to a single-pulse energy of 12.55 nJ.