We report for the first time, to our knowledge, the diode-pumped continuous-wave (CW) thin-disk Yb³⁺-doped Lu₂O₃ (Yb:LO) laser at 1 034 nm and the second-harmonic generation at 517 nm. With a 6.3% output coupler, the maximum output power is 1.17 W under a pump power of 18.5 W. Moreover, the intracavity second-harmonic generation (SHG) is also achieved with power of 193 mW at 517 nm by using an LiB₃O₅ (LBO) nonlinear crystal. The beam quality factor M ² is about 1.28. The fluctuation of the output power is about 3% in 1 h.