This paper analytically investigates global and local instability in sandwich columns with monolithic aluminium facesheets and Face-Centered Body-Centered Cubic (FBCC) lattice cores produced by additive manufacturing. To account for core transverse compressibility and its influence on face local instability characterized by wrinkling, a higher-order solution is developed. Finite Element simulations using 3D solid elements for the facesheets and beam elements for the core under various boundary conditions validate the model. Analytical and numerical results show close agreement, accurately predicting global (in-plane/out-of-plane) and local (intracell/wrinkling) modes. Boundary conditions strongly affect global instability, whereas local instability depends mainly on geometric parameters. The proposed method offers an efficient and accurate tool for predicting instability in lattice-core sandwich columns for lightweight structural applications.