Energetics and kinetics of Li insertion into c-Si and a-Si systems are investigated using the density functional (DFT) theory calculations and kinetic Monte Carlo (KMC) simulations. DFT formation energies show the mechanism of phase separation between crystalline silicon and amorphous lithium silicide. Both crystalline and amorphous Si show similar trends in volume expansion and phase transition under lithiation, and kinetics of Li diffusion in bulk silicon (from DFT and KMC) shows a big difference between c-Si and a-Si. The Li migration barrier is 0.6 eV in c-Si, and quickly decreases to 0.4 eV under increasing Li concentration or Si volume expansion. To simulate Li diffusion in amorphous silicon using KMC, we have developed a formulation for environment dependent migration energy barriers of Li in a-Si using a volume dependent function. KMC simulations are performed for Li diffusion in both c-Si and a-Si, and the diffusion coefficient of Li in a-Si is an order of magnitude larger than in c-Si. These studies help to understand mechanisms of lithiation with atomic scale details and elucidate the phase separation between c-Si and lithium silicide.