Lie algebra model theory studies the closure \(\overline{{\mathcal O}(\lambda)}\) of the \(\text{Gl}_n({\mathbb C})\)-orbit in the variety \({\mathcal L}^n\) of Lie algebra laws of a law \(\lambda\) on \({\mathbb C}^n\) using nonstandard analysis. In this context, given a Lie algebra law \(\lambda\), a {contraction} of \(\lambda\) is a law \(\mu\) with \(\mu\in\overline{{\mathcal O}(\lambda)}\). On the other hand, a {perturbation} of \(\lambda\) in \({\mathcal L}^n\) is a \(\mu\in{\mathcal L}^n\) such that the absolute value of the difference of the structure constants of \(\lambda\) and \(\mu\) over a standard basis is smaller than any strictly positive real standard. Keeping this in mind, a Lie algebra \({\mathfrak g}_0=({\mathbb C}^n,\mu_0)\) is called a {model} relative to a property \((P)\) if any Lie algebra law \(\mu\) satisfying \((P)\) contracts to \(\mu_0\) and any perturbation of \(\mu_0\) satisfies \((P)\). The property \((P)\) studied in the article under review is the one to be {Frobenius}, i.e. the property that there exists a linear form \(\omega\in{\mathfrak g}^*\) on the \(2n\)-dimensional Lie algebra \({\mathfrak g}\) whose differential is symplectic, i.e. \(\omega^n\not=0\). A family \(F\) of Lie algebras satisfying a property \((P)\) is called a {multiple model} relative to \((P)\) if any Lie algebra satisfying \((P)\) contracts to a member of \(F\) and any perturbation of a member of \(F\) satisfies \((P)\). \textit{M. Goze} found in [C. R. Acad. Sci., Paris, Sér. I 293, 425--427 (1981; Zbl 0483.53012)] a multiple model for the above stated property \((P)\). The authors of the present article compute first and second cohomology space of the Lie algebras in this family with respect to the adjoint representation. Furthermore, they compute the first obstruction for infinitesimal deformations to be prolonged which turns out to be zero.