  In the interest of finding the minimum additive generating set for the set of
$\boldsymbol{s}$-lecture hall partitions, we compute the Hilbert bases for the
$\boldsymbol{s}$-lecture hall cones in certain cases. In particular, we compute
the Hilbert bases for two well-studied families of sequences, namely the $1\mod
k$ sequences and the $\ell$-sequences. Additionally, we provide a
characterization of the Hilbert bases for $\boldsymbol{u}$-generated Gorenstein
$\boldsymbol{s}$-lecture hall cones in low dimensions.
