Lithium tetraborate (LB4) is a nonlinear crystal that has very low optical absorption in the visible and ultraviolet range. Hence, it is a very interesting material for nonlinear conversion experiments, particularly in whispering gallery mode (WGM) resonators. Here, we show theoretically that second-harmonic generation is possible over a wide range of pump wavelengths ($488\,\textrm{nm}$ to $3320\,\textrm{nm}$) in an $ x $-cut LB4 WGM resonator. We also demonstrate this experimentally at three different pump wavelengths ($1560\,\textrm{nm}$, $795\,\textrm{nm}$, and $517\,\textrm{nm}$). We find a reasonable conversion efficiency of $0.2\,\% / \textrm{mW}$ for the generation of UV light at $258.5\,\textrm{nm}$. This is possible due to the high-quality factors on the order of $5\times 10^{7}$ and the use of the so-called selective coupling method.