Two distinct and complementary in nature numerical methods for the inverse engineering and generation of lattice metamaterials are elaborated. The first is based on the combination of homogenization schemes with genetic algorithms and it allows for the exploitation of the complete set of parameters contained in a target compliance tensor. Thereupon, unit-cell lattice patterns that meet macroscale target elastic, shear, Poisson’s ratio and normal to shear strain coupling performances are inversely identified. The methodology can be used to identify either specific relative density metamaterial designs or allow for relative density adjustments so that the mechanical objectives are optimally satisfied. Designs within and beyond orthotropy are parsed and different case-study examples are provided, highlighting the potential of the formulation to capture a wide range of effective metamaterial behaviours. In the second, complementary numerical analysis technique, a wide range of optimized lattice architectures with different effective mechanical properties is generated. Thereupon, variational, convolutional network graph-based auto-encoders are developed, capable of accurately embedding the mechanical behaviour of lattice structures with a large number nodal connectivity. The corresponding formulation and computational cost are thoroughly analysed, while the applicability limitations are discussed. In all cases, 3D printing is employed to engineer and experimentally probe the mechanical properties of the periodic metamaterial specimens identified, highlighting the manufacturing feasibility and robustness of the underlying numerical schemes, as a function of the manufacturing limits of polymer 3D-Printing (Stratasys) and Powder Bed Fusion technologies.