The understanding of lithium solvation and transport in ionic liquids is important due to the possible applications in electrochemical devices. Using first principles simulations aided with the metadynamics approach we study the free energy landscape for lithium at infinite dilution conditions in ethylammonium nitrate, a protic ionic liquid. We analyze the local structure of the liquid around the lithium cation and find a quantitative picture in agreement with experimental findings. Our simulations show that the lowest two free energy minima correspond to conformations with the lithium solvated either by 3 or 4 nitrates ions with a transition barrier between them of 0.2 eV. Other less probable conformations having a different solvation pattern are also investigated.