Transverse-field muon-spin rotation measurements performed on two samples of LiFeAs demonstrate that the superfluid stiffness of the superconducting condensate in relation to its superconducting transition temperature is enhanced compared to other pnictide superconductors. Evidence is seen for a field-induced magnetic state in a sample with a significantly suppressed superconducting transition temperature. The results in this system highlight the role of direct Fe-Fe interactions in frustrating pairing mediated by antiferromagnetic fluctuations and suggest that, in common with other pnictide superconductors, the system is close to a magnetic instability.