An R-on-1 laser-induced damage-threshold (LIDT) testing method was applied to test coated and uncoated magnesium oxide-doped periodically poled lithium niobate samples pumped by femtosecond Yb:KGW laser pulses at kilohertz and megahertz pulse repetition rates. LIDT values decreased by ∼1.5 and ∼38 times when increasing repetition rate from 100 to 571 kHz and to 76 MHz, respectively. We also investigated nonlinear absorption changes in lithium niobate crystals at the pulse repetition range from 60 to 600 kHz with trains consisting of 100 identical femtosecond pulses. Laser beam transmission in the crystal experienced a drop of ∼18  %   from initial pulses of train to the next 40 pulses at intensities 40% to 15% lower than LIDT due to nonlinear absorption of 220 fs duration pulses at 1.03  μm.