Tensegrity lattices are networks of axially loaded members designed to efficiently use material and exhibit properties such as minimum mass load-carrying or energy absorption capabilities. This work entails the modeling and design of tensegrity “D-bar” lattices with specified orthotropic compressive strength. The objectives for the design of the lattices include minimum mass density and minimum error between the orthotropic coefficients of thermal expansion (CTEs) of the lattice and given target values. The studied D-bar structures are formed by joining two equal pyramids base-to-base where tensile strings form the edges of the pyramid bases and compressive bars form the remaining edges. Orthorhombic lattices having D-bars as their edges are designed to support compressive forces and exhibit positive, zero, or negative CTE values along their three principal directions. It is investigated how the geometry of the individual D-bar components may be adjusted, for the given compressive strength, to prevent local yielding and buckling failure with the minimum required material. Analytical formulas for the minimum density and the CTE of the D-bar lattices are provided, and a numerical framework for the integration of these formulas along with size and topological constraints is developed. Design trade-offs between minimum lattice density and minimum error from the target CTE, which are found to be competing structural performance metrics, are visualized and investigated.