Characteristics of diode-wing-pumped highly efficient Tm:LuAG lasers running both in continuous wave (CW) and electro-optical Q-switching regimes have been investigated. Using a simple plane-plane cavity, a maximum CW output power of 8.5 W has been achieved with a corresponding slope efficiency of 44.5% by "wing pumping" at 790 nm. With a V-shaped cavity, a diode-wing-pumped MgO:LiNbO3 crystal based electro-optically Q-switched Tm:LuAG laser at 2022.9 nm delivered a maximum pulse energy of 10.8 mJ and a minimum pulse width of 52 ns at a corresponding repetition rate of 100 Hz. To the best of our knowledge, the achieved CW output power and Q-switched pulse energy have both set records for all-solid-state Tm:LuAG lasers, which well reveals an efficient way to generate high-power and high-energy lasers at 2 μm wavelength.