Multi-material additive manufacturing has provided a compelling opportunity to design and realize multi-material structures in a use-inspired manner, with a wide range of applications in many realms of engineering. While multimaterial additive manufacturing enables finely programmed heterogeneity, there remains no robust and objective-driven framework to assign materials across complex architectures under practical constraints. We introduce Data-Driven-Design as a robust computational framework for multi-material lattice design, optimized with respect to a prescribed performance objective. The framework relies on representing physical constraints, material data, and design objectives as sets in a phase space and formulating the material selection problem as a distance minimization problem among the encoded sets. We showcase the approach in multi-material design of viscoelastic lattices provided with measurements of complex moduli as a function of frequency with the design objective of maximizing dissipation. For our numerical experiments, we import dynamic viscoelasticity measurement for twenty five different materials from literature, and show that multi-material designs can match or outperform the dissipation obtained from homogeneous designs made of the most dissipative material among the data registry. In a finite lattice example, we show that design yields a mechanical dissipation with 3-fold increase compared to best homogeneous design from a limited collection of materials. Beyond viscoelastic lattices, the framework generalizes naturally to multi-physics and multi-objective metastructure design, offering a unified, data-driven approach to optimal material selection under complex constraints.