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We propose a lattice of skewed transmission lines to implement a full effective material tensor. First we show, using transformation electromagnetics, how a skewed lattice will introduce off-diagonal components in the material tensor. We then show how this can be extended to a transmission-line network placed on a skewed lattice, using periodic analysis of a 2-D transmission-line network. We also show how to design a 2-D transmission-line unit cell to implement a full-material tensor for 2-D propagation. We confirm our results using full-wave simulation of a unit cell, as well as full-wave simulation of refraction in a transmission-line network between an isotropic effective medium and a anisotropic effective medium. Finally, we show how this idea can be extended to 3-D unit cells for transformation electromagnetics applications.