The potential of (N_{g}) -cut monoclinic Yb: and Tm:KLu(WO4)2 laser crystals is analyzed from the point of view of thermal lensing, including athermal behavior, unique laser mode stabilization by polarization-switching and potential for microchip operation. To this aim, we characterize dispersion and direction dependence of the generalized thermo-optic coefficients, (Delta ) , for the light polarizations, (E|N_{m}) and (N_{p}) , and calculate sensitivity factors of the thermal lens for wide range of experimental conditions, including crystal temperature, laser wavelength, pump spot radius, as well as their relation to probe beam measurements. The polarization-switching between (N_{m}) and (N_{p}) oscillating states is realized for a Tm:KLu(WO4)2 crystal and explained on the basis of spectroscopic properties, mode-matching and cavity stability. The thermal lens properties for microchip Tm:KLu(WO4)2 laser are also calculated.