We report the first, to the best of our knowledge, laser operation of acentric Yb3+-doped La2CaB10O19 (Yb:LCB) crystal since its discovery in 1998. The polarized absorption and emission cross-section spectra of Yb:LCB were calculated at room temperature. Using a fiber-coupled 976 nm laser diode (LD) as the pump source, we realized effective dual-wavelength laser generation at around 1030 and 1040 nm. The highest slope efficiency of 50.1% was obtained in the Y-cut Yb:LCB crystal. In addition, via resonant cavity design on a phase-matching crystal, a compact self-frequency-doubling (SFD) green laser at 521 nm was also realized in a single Yb:LCB crystal with an output power of 152 mW. These results promote Yb:LCB as a competitive multifunctional laser crystal, especially for highly integrated microchip laser devices ranging from the visible to the near-infrared regime.