The differential cross sections for small-angle proton elastic scattering on the 6,8,9,11Li nuclei at energies near 700 MeV/nucleon were measured in inverse kinematics using secondary nuclear beams at GSI Darmstadt. The hydrogen-filled ionization chamber IKAR was employed as target and recoil proton detector. For determining the nuclear matter radii and radial matter distributions, the measured cross sections have been analysed with the aid of the Glauber multiple-scattering theory. The nuclear matter distribution deduced for 11Li exhibits a very pronounced halo structure, the matter radius of 11Li being significantly larger than those of the 6,8,9Li isotopes. The data on 8,9Li are consistent with the existence of sizable neutron skins in these nuclei. The obtained data allow for a test of various theoretical model calculations of the structure of the studied neutron-rich nuclei.