Measurements of the trap loss rate in ultra-cold magneto-optically trapped \sp6Li and \sp7Li are presented and compared. Clear evidence is presented for two different trap loss mechanisms involving inelastic collisions between one ground state atom and one excited state atom. The fine-structure changing (FSC) mechanism, in which the excited state atom changes fine-structure level during a collision, is seen to dominate the rate at low trap laser intensities. However, as the intensity is increased, the trap becomes sufficiently deep to be able to contain the products of FSC collisions and this mechanism no longer contributes to trap loss. It is a unique aspect of Li that the energy imparted to an atom in a FSC collision is in a range that may be recaptured with experimentally attainable trap parameters. When the products of all FSC collisions remain trapped, only the radiative escape (RE) trap loss mechanism, due to the emission of a less energetic photon than the initial excitation photon, contributes to the trap loss rate. At small detunings, the rate of the RE trap loss mechanism is seen to be over two orders-of-magnitude smaller than the FSC rate. The FSC trap loss rate for \sp6Li and \sp7Li were found to be largest at smaller detunings and of comparable magnitude in \sp6Li and \sp7Li. The RE trap loss rate in \sp6Li was seen to be roughly four times the RE trap loss rate in \sp7Li. To understand better the dynamics of trap loss and magneto-optical traps in general, a sophisticated model of magneto-optical trap kinetics has been developed. This model has demonstrated that most critical factor determining the maximum velocity an atom may have and yet remained trapped is the initial atom's frame detuning, Δ - k v, where Δ is the trap laser detuning, k is the propagation vector of the trap beam most nearly anti-parallel to v, the atom's velocity. All else being equal, minimizing the magnitude of this quantity maximizes the velocity that a trap will retain. More detailed results of this model are also presented.