Adiabatic frequency conversion has some key advantages over nonlinear frequency conversion. No threshold and no phase-matching conditions need to be fulfilled. Moreover, it exhibits a conversion efficiency of 100% down to the single-photon level. Adiabatic frequency conversion schemes in microresonators demonstrated so far suffer either from low quality factors of the employed resonators resulting in short photon lifetimes or small frequency shifts. Here, we present an adiabatic frequency conversion (AFC) scheme by employing the Pockels effect. We use a non-centrosymmetric ultrahigh-Q microresonator made out of lithium niobate. Frequency shifts of more than 5GHz are achieved by applying just 20V to 70-micrometer-thick crystal. Furthermore, we demonstrate that already with the same setup positive and a negative frequency chirps can be generated. With this method, by controlling the voltage applied to the crystal, almost arbitrary frequency shifts can be realized. The general advances in on-chip fabrication of lithium-niobate-based devices make it feasible to transfer the current apparatus onto a chip suitable for mass production.