This paper concerns compliance minimization and projection of coated structures with orthotropic infill material in 2D. The purpose of the work is two-fold. First, we introduce an efficient homogenization-based approach to perform topology optimization of coated structures with orthotropic infill material. The design space is relaxed to allow for a composite material description, which means that designs with complex microstructures can be obtained on relatively coarse meshes. Second, a method is presented to project the homogenization-based designs on a fine but realizable scale. A novel method to adaptively refine the lattice structure is presented to allow for a regular spacing of the infill. Numerical experiments show excellent behavior of the projected designs, with structural performance almost identical to the homogenization-based designs. Furthermore, a reduction in computational cost of at least an order of magnitude is achieved, compared to a related approach in which the infill is optimized using a density-based approach.