We report on continuous-wave laser operation of Tb3+:LiLuF4 under UV pumping. More than five times higher absorption cross sections in the UV allow for shorter gain media, which are required for future high-power diode pumping. The cross-relaxation process is found to efficiently populate the upper laser level 5D4 at doping concentrations typically used in Tb3+-doped gain media. Pumping with a frequency doubled Ti:sapphire laser at 359 nm enables laser operation in the green and yellow spectral range with slope efficiencies of 41% and 20%, respectively, at optical-to-optical efficiencies a factor of two higher than under cyan-blue pumping.