The System for Measuring Overlap with Gas (SMOG2) at the LHCb detector enables the study of fixed-target ion-ion collisions at relativistic energies (sqrt[s_{NN}]∼100 GeV in the center of mass). With input from ab initio calculations of the structure of ^{16}O and ^{20}Ne, we compute 3+1D hydrodynamic predictions for the anisotropic flow of Pb+Ne and Pb+O collisions to be tested with upcoming LHCb data. This will allow the detailed study of quark-gluon plasma formation as well as experimental tests of the predicted nuclear shapes. Elliptic flow (v_{2}) in Pb+Ne collisions is greatly enhanced compared to the Pb+O baseline due to the shape of ^{20}Ne, which is deformed in a bowling-pin geometry. Owing to the large ^{208}Pb radius, this effect is seen in a broad centrality range, a unique feature of this collision configuration. Larger elliptic flow further enhances the quadrangular flow (v_{4}) of Pb+Ne collisions via nonlinear coupling, and impacts the sign of the kurtosis of the elliptic flow vector distribution (c_{2}{4}). Exploiting the shape of ^{20}Ne proves thus an ideal method to investigate the formation of quark-gluon plasma in fixed-target experiments at LHCb, and demonstrates the power of System for Measuring Overlap with Gas as a tool to image nuclear ground states.