The potential energy surfaces of the LinSi4- (n = 0-5) clusters were explored using the Kick Coalescence method. We found that, for those systems with n <= 2, the butterfly and parallelogram Si-4(2-) kernels prevail as building blocks; however, when n >= 3, the Si-4(4-) tetrahedral kernel, which is commonly found in heavier alkali monosilicides, MSi (M = Na, K, Rb, Cs), arises as the prevailing building block. In addition, by a natural population analysis (NPA) we found that the maximum charge transfer -4 from Li atoms to Si atoms is attained when n = 3. The addition of more Li atoms to the Si-4(4-) system does not increase the charge transfer, but keeps it almost constant at the maximum value. We also calculated theoretical vertical electron detachment energies (VDEs) for low-lying isomers of the LinSi4- (n = 0-4) clusters in order to facilitate their experimental identification.