Tunable light sources are a key enabling technology for many applications such as ranging, spectroscopy, optical coherence tomography, digital imaging and interferometry. For miniaturized laser devices, whispering gallery resonator lasers are a well-suited platform, offering low thresholds and small linewidths, however, many realizations suffer from the lack of reliable tuning. Rare-earth ion-doped lithium niobate offers a way to solve this issue. Here we present a single-frequency laser based on a neodymium-doped lithium niobate whispering gallery mode resonator that is tuned via the linear electro-optic effect. Using a special geometry, we suppress higher-order transverse modes and hence ensure single-mode operation. With an applied voltage of just 68 V, we achieve a tuning range of 3.5 GHz. The lasing frequency can also be modulated with a triangular control signal. The freely running system provides a frequency and power stability of better than Δ ν=20MHz and 6 %, respectively, for a 30-minute period. This concept is suitable for full integration with existing photonic platforms based on lithium niobate.