We study the moduli space of triples (C,L₁,L₂) consisting of quartic curves C and lines L₁ and L₂. 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 t₁ and t₂ which correspond to the choice of a linearization. For t₁=t₂=1 we describe the GIT moduli explicitly and relate it to the construction via K3 surfaces
