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Compliant joints are flexible elements that allow displacement due to the elastic deformations they experience under the action of external loading. The flexible parts responsible for these displacements are known as flexure hinges. Displacement, or motion range, in compliant joints depends on the stiffness of the flexure hinges and can be tailored through various parameters, including the overall dimensions, the base material, and the distribution within the hinge. Considering the distribution, we propose the stiffness modification of a compliant cross-axis joint via the use of lattice mechanical metamaterials. Due to the wide range of parameters that influence the stiffness of a lattice, different machine learning algorithms (artificial neural networks, support vector machine, and Gaussian progress regression) were proposed to forecast these parameters. Here, the machine learning algorithm with the best forecasting was the Gaussian progress regression; this algorithm has the advantage of well-tuning even with small regression databases, allowing these functions to more easily adjust to suit specific data, even if the dataset is small. Hexagonal, re-entrant, and square lattices were studied as flexure hinges. For each, the effect of the unit cell size and its orientation with respect to the principal axis on the effective stiffness were studied via computational and laboratory experiments on additively manufactured samples. Finite element predictions resulted in good agreement with the experimentally obtained data. As a result, using lattice-flexure hinges led to increments in displacement ranging from double to ten times those obtained with solid hinges. The most suitable machine learning algorithm was the Gaussian progress regression, with a maximum error of 0.12% when compared to the finite element analysis results.