Excitation functions have been measured for reaction products from the $^{6}\mathrm{Li}$ and $^{7}\mathrm{Li}$ induced reactions $^{6}\mathrm{Li}$+$^{12}\mathrm{C}$, $^{6}\mathrm{Li}$+$^{13}\mathrm{C}$, $^{7}\mathrm{Li}$+$^{12}\mathrm{C}$, and $^{7}\mathrm{Li}$+$^{13}\mathrm{C}$. These data cover the energy range from ${E}_{\mathrm{lab}}=9 \mathrm{to} 36$ MeV. It was found that the maximum fusion cross sections for these reactions are 780 and 770 mb for the $^{6}\mathrm{Li}$+$^{12}\mathrm{C}$ and $^{6}\mathrm{Li}$+$^{13}\mathrm{C}$, respectively, and 960 and 930 mb for the $^{7}\mathrm{Li}$+$^{12}\mathrm{C}$ and $^{7}\mathrm{Li}$+$^{13}\mathrm{C}$, respectively. The relative uncertainties for these maximum fusion cross sections are about 5%. Comparisons between optical model calculations of the total reaction cross sections and the measured fusion cross sections indicate that total fusion cross sections are substantially smaller than the total reaction cross sections for all four reactions at all energies. For each of the four entrance channels, energy and angular distributions have been measured at four energies for individual mass groups between $A=9 \mathrm{and} 19$ u. Most of these products appear to be evaporation residues. The critical angular momenta deduced from the experimental fusion cross sections are discussed in terms of entrance channel and compound nucleus limitation models for compound nucleus formation. The individual mass groups are discussed in terms of systematics for evaporation residues.NUCLEAR REACTIONS $^{6}\mathrm{Li}$+$^{12}\mathrm{C}$, ${E}_{^{6}\mathrm{Li}}=10 \mathrm{to} 36$ MeV; $^{6}\mathrm{Li}$+$^{13}\mathrm{C}$, ${E}_{^{6}\mathrm{Li}}=9.23 \mathrm{to} 35.08$ MeV; $^{7}\mathrm{Li}$+$^{12}\mathrm{C}$, ${E}_{^{7}\mathrm{Li}}=10 \mathrm{to} 38$ MeV; $^{7}\mathrm{Li}$+$^{13}\mathrm{C}$, ${E}_{^{7}\mathrm{Li}}=10 \mathrm{to} 34$ MeV, measured $\frac{{d}^{2}\ensuremath{\sigma}}{d\ensuremath{\Omega}\mathrm{dE}}$ for reaction products from $A=9 \mathrm{to} 19$. Extracted ${\ensuremath{\sigma}}_{\mathrm{fus}}$.