We have performed a kinematically complete measurement of the Coulomb dissociation of 28 MeV/nucleon Li into Li and two neutrons by a Pb target. From the energies and angles of the emitted neutrons and of Li, the excitation energy E of Li was determined on an event-by-event basis, and the Coulomb dissociation cross section as a function of excitation energy was constructed.The photonuclear cross section o~q (E) and the dipole strength function dB(El)/dE were determined from the Coulomb dissociation cross section. o~q(E) has a peak at E = 1.0 MeV and a width I = 0.8 MeV. These parameters are consistent with the picture of a soft dipole mode. However, a significant post-breakup Coulomb acceleration of Li suggests instead a direct breakup. The complete kinematical measurement also allowed neutron and Li momentum distributions to be constructed in the rest frame of the Li. The momentum distributions were fitted with Gaussian functions, yielding width parameters o& = 18 + 4 MeV/c and o"=13 + 3 MeV/c. A more general feature of the breakup mechanism of Li could be deduced from these measurements. It was found that the Li and neutron momentum distributions and the neutron-neutron relative momentum distribution could be reproduced if the Li excitation energy was partitioned between the Li and the neutrons by a three-body phase space distribution. This indicates there is no directional correlation between the halo neutrons, and shows that the halo neutrons do not exist as a dineutron bound to a Li core. PACS number(s): 25.70. De, 21.10.Gv, 25.20.Dc, 25.60.+v