Lithium niobate (LN) is widely used and established in nonlinear and integrated optics. Efficient nonlinear frequency conversion is enabled by quasi-phase matching of the interacting waves through periodic poling of the crystal domains. For realizing miniaturized optical devices, the application of lithium niobate on insulator (LNOI) substrates becomes increasingly important. LNOI consists of a LN thin film on top of a silica layer [1]. Using the common electric field poling [2] through an LNOI wafer is impeded by the insulating silica layer. Therefore, only surface poling techniques can be employed [3-5]. Here, the electric field is applied parallel to the substrate surface along the in-plane z-axis of the x-cut LN film. In this work, we present a systematic study of the surface domain engineering of bulk LN and LNOI, aiming to optimize the quality of the domain patterns.