We report on fabrication of dual-line waveguides in Yb:LuAG crystal by 1030-nm femtosecond laser inscription, 450 fs pulses at a 100 kHz repetition rate. The efficient single-mode guidance is demonstrated in the type II waveguide structures when propagating light along both TE and TM polarization at 632.8 nm and 1064 nm. Based on the configuration, the minimum propagation loss of the 18-µm width waveguide is determined to be 0.55 dB/cm at wavelength of 632.8 nm. Both the lattice-damaged tracks and strain-affected regions are characterized by means of the confocal micro-Raman spectroscopy. In combination with beam propagation calculations, we quantitatively determine the corresponding contribution of each effect to the refractive-index field of the fabricated waveguides.