We present a high-peak-power SESAM-modelocked thin-disk laser (TDL) based on the gain material Yb-doped lutetia (Yb:Lu2O3), which exceeds a peak-power of 10 MW for the first time. We generate pulses as short as 534 fs with an average power of 90 W and a peak power of 10.1 MW, and in addition a peak power as high as 12.3 MW with 616-fs pulses and 82-W average power. The center lasing wavelength is 1033 nm and the pulse repetition rates are around 10 MHz. We discuss and explain the current limitations with numerical models, which show that the current peak power is limited in soliton modelocking by the interplay of the gain bandwidth and the induced absorption in the SESAM with subsequent thermal lensing effects. We use our numerical model which is validated by the current experimental results to discuss a possible road map to scale the peak power into the 100-MW regime and at the same time reduce the pulse duration further to sub-200 fs. We consider Yb:Lu2O3 as currently the most promising gain material for the combination of high peak power and short pulse duration in the thin-disk-laser geometry.