The unbound isotopes 10Li, 12Li and 13Li have been observed after nucleon-knockout reactions at relativistic energies with 11Li and 14Be beams impinging on a liquid hydrogen target. The channels , and were analysed in the ALADIN-LAND setup at GSI. The 10Li data confirm earlier findings, while the 12Li and 13Li nuclei were observed for the first time. The relative-energy spectrum shows that the ground state of 12Li can be described as a virtual s-state with a scattering length of −13.7(1.6) fm. A broad energy spectrum was found for the channel. Based on the assumption that the relative-energy spectrum is dominated by a correlated background presumably stemming from initial correlations in the 14Be ground-state, evidence for a 13Li resonance at 1.47(31) MeV above the threshold with a width around 2 MeV has been found.