  We study the moduli space of triples $(C, L_1, L_2)$ consisting of quartic
curves $C$ and lines $L_1$ and $L_2$. Specifically, we construct and compactify
the moduli space in two ways: via geometric invariant theory (GIT) and by using
the period map of certain lattice polarized $K3$ surfaces. The GIT construction
depends on two parameters $t_1$ and $t_2$ which correspond to the choice of a
linearization. For $t_1=t_2=1$ we describe the GIT moduli explicitly and relate
it to the construction via $K3$ surfaces.
