Laser cooling to micro-Kelvin temperatures requires a laser with active frequency stabilization. The linewidth of an atomic transition sets a lower bound on the Doppler cooling temperature. The 2s-2p transition in lithium-6 has a Doppler temperature of ~140 μK In contrast, the 2s-3p transition has a narrower linewidth and thus provides a lower temperature limit of ~20 μK. We present a method for stabilizing a laser to an atomic line in a vapor cell using modulation transfer spectroscopy and a home-built lock-in amplifier. Our results demonstrate successful locking of a 323 nm laser to the 2s-3p transition. The stabilized laser provides a second stage of magneto-optical trapping that results in a factor of ∼5 increase in the phase space density before evaporating to degeneracy in an optical dipole trap.