A Lagrange variety of a symplectic manifold \(E\) of dimension \(2n\) is a subset \(\Lambda\) of \(E\) that admits a statification into strata of dimension at most \(n\) such that the symplectic form of \(E\) vanishes on each of the strata. Given a Lagrange variety \(\Lambda\subset E\), two Lagrange fibrations \(\pi, \pi':E\to Y\) over a smooth manifold \(Y\) are called \(\Lambda\)-equivalent if there is a symplectic diffeomorphism \(\tau\) of \(E\) preserving \(\Lambda\) and a diffeomorphism \(\sigma\) of \(Y\) such that \(\pi'\circ\tau=\sigma\circ\pi\). The simplest singularity of a Lagrange variety is the first open Whitney umbrella \(\Lambda_1\). The authors present a classification up to \(\Lambda_1\)-equivalence of the simple stable germs of Lagrange fibrations at the first open Whitney umbrella. This extends the Arnold ADE-classification given for smooth Lagrange varieties.