We confine $4\ifmmode\times\else\texttimes\fi{}{10}^{8}$ fermionic ${}^{6}\mathrm{Li}$ atoms simultaneously with $9\ifmmode\times\else\texttimes\fi{}{10}^{9}$ bosonic ${}^{7}\mathrm{Li}$ atoms in a magneto-optical trap based on an all-semiconductor laser system. We optimize the two-isotope sample for sympathetic evaporative cooling. This is an essential step towards the production of a quantum-degenerate gas of fermionic lithium atoms.