We present an efficient scheme to implement a gray optical molasses for sub-Doppler cooling of $^{6}$Li atoms with minimum experimental overhead. To integrate the $D_1$ light for the gray molasses (GM) cooling into the same optical setup that is used for the $D_2$ light for a standard magneto-optical trap (MOT), we rapidly switch the injection seeding of a slave laser between the $D_2$ and $D_1$ light sources. Switching times as short as $30,mutextrm{s}$ can be achieved, inferred from monitor optical beat signals. The resulting low-intensity molasses cools a sample of $N=9times10^8$ atoms to about $60,mutextrm{K}$. A maximum phase-space density of $rho=1.2times10^{-5}$ is observed. On the same setup, the performance of the GM is compared to that of narrow-line cooling in a UV MOT, following the procedure in Sebastian et al. (2014). Further, we compare the production of a degenerate Fermi gas using both methods. Loading an optical dipole trap from the gray molasses yields a quantum degenerate sample with $3.3times10^5$ atoms, while loading from the denser UV MOT yields $2.4times10^6$ atoms. Where the highest atom numbers are not a priority this implementation of the gray molasses technique yields sufficiently large samples at a comparatively low technical effort.
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