Calculations are presented for the double photoionization (with excitation) and triple photoionization of the Li atom. The motion of all three electrons is treated equally by solving the time-dependent Schrödinger equation in nine dimensions. A radial lattice is used to represent three of the nine dimensions, while a coupled channel expansion is used to represent the other six dimensions. Probabilities for photoionization are obtained by t--> infinity projection onto fully antisymmetric spatial and spin functions. Double photoionization cross sections for lithium leaving the ion in the 1s, 2s, and 2p states are presented. Good agreement is found with the measurements of Huang et al. [Phys. Rev. A 59, 3397 (1999)]] for the total double photoionization cross section and with the measurements of Wehlitz et al. [Phys. Rev. Lett. 81, 1813 (1998)]] for the triple photoionization cross section.