An analytical framework for harnessing buckling instabilities in metamaterial lattices is presented. The framework comprises systematic procedures where mechanical rigid-link--spring models are generically constructed and analysed in combination with a path-following solver. The nonlinear mechanical response of lattices is tailored through specifically derived cross-sectional modifications making use of explicit incremental relationships between buckling loads and stiffness parameters employed within an optimisation routine. The resulting post-buckling behaviour is tuned by triggering more favourable deformation modes, alongside requiring buckling loads to be sufficiently separated to suppress deleterious modal interaction phenomena. The framework is verified through nonlinear finite element simulations. The present approach is demonstrated to provide an efficient and robust procedure for developing improved lattice designs that produce enhanced mechanical performance under large deformations.