Thermal lensing is studied in Yb:KLu(WO 4 ) 2 crystals cut along the three optical indicatrix axes, N p , N m and N g . The cut along the N g -axis is the only one that provides a pure positive thermal lens with the sensitivity factors M = 3.5 and 2.8 m −1 W −1 (w p = 100 μm) for the mg-and pg-planes, respectively, and a low astigmatism degree, S/M < 20%. Both N p -cut and N m -cut crystals produce different-signed lens with at least six-times stronger astigmatism. This behavior is related to the anisotropy of the photo-elastic effect. A CW Yb:KLu(WO 4 ) 2 microchip laser delivering a maximum output power of 992 mW at 1051 nm with a slope efficiency of 40%, and possessing low spatial distortions of the laser beam and M 2 < 1.1, is realized on the basis of N g -cut crystal.