We present a study of second harmonic generation (SHG) and third harmonic generation (THG) in lithium triborate (LBO) crystals using a high-energy, 10-J-class, 10 Hz Yb:YAG laser system. We achieved high conversion efficiencies of 75% for SHG and 56% for THG for Gaussian-like temporal pulse shapes and top-hat-like beam profiles. The angular and temperature dependence of the LBO crystals were measured and validated through numerical simulations. The SHG process exhibited an angular acceptance bandwidth of 1.33 mrad and a temperature acceptance bandwidth of 2.61 K, while the THG process showed 1.19 mrad and 1.35 K, respectively. Additionally, long term stability measurements revealed RMS energy stabilities of 1.3% for SHG and 1.24% for THG. These results showcase the reliability of LBO crystals for high-energy, high-average-power harmonic generation. The developed system offers automated switching between harmonics provided at the system output. The system can be easily adapted to Nd:YAG based pump lasers as well.