We investigate Kerr lens mode locking of Yb:Lu_2O_3 thin-disk laser oscillators operating in the sub-100-fs regime. Pulses as short as 35 fs were generated at an average output power of 1.6 W. These are the shortest pulses directly emitted from a thin-disk laser oscillator. The optical spectrum of the 35-fs pulses is almost 3 times broader than the corresponding emission band of the gain crystal. At slightly longer pulse duration of 49 fs, we achieve an average power of 4.5 W. In addition, 10.7 W are obtained in 88-fs pulses, which is twice higher than the previous power record for ultrafast thin-disk lasers generating pulses shorter than 100 fs. Our results prove that Kerr lens mode-locked Yb:Lu_2O_3 thin-disk lasers are a promising technology for further average power and pulse energy scaling of ultrafast high-power oscillators operating in the sub-100-fs regime.