In this paper, we address the problem of solving accurately gas-liquid compressible flows, without pressure oscillations at the gas-liquid interface. We introduce a new Lagrange-projection scheme based on a random sampling technique of Chalons and Goatin. We compare it to a Ghost Fluid approach introduced previously. Despite the non-conservative feature of the schemes, we observe the numerical convergence towards the relevant weak solution, for shock-contact interaction test cases. Finally, we apply the new scheme to the computation of the oscillations of a spherical air bubble inside water.