Recently, we have proposed a game of minimizing static (player 1) and dynamic (player 2) compliance, respectively, by using a multi-scale topology optimization framework for TPMS-based lattice structures. In this work, we demonstrate the idea of the game for Schwarz-D lattice structures, both shell and frame-based. Player 1 establish the optimal macro layout by minimizing the static compliance for a given micro layout delivered from player 2, and player 2 finds the optimal micro layout (grading of the TPMS-based lattice structure) by minimizing the dynamic compliance for a given macro layout from player 1. The two multi-scale topology optimization formulations are obtained by using two density variables in each finite element. The first variable is the standard topology optimization macro density variable, which defines if the element should be treated as a void or contain the graded lattice structure by letting this variable be governed by the rational approximation of material properties (RAMP) model. The second variable is the local relative lattice density, and it sets the effective orthotropic elastic properties of the element, which in turn are obtained by using numerical homogenization of representative volume elements of the Schwarz-D lattice structure. Player 1 follows the standard compliance problem formulated in the first density variable using graded lattice structures from player 2. Furthermore, player 2 grades the lattice structure by solving the dynamic compliance problem for a harmonic load formulated in the second variable for a macro-layout presented by player 1. The game is implemented for three-dimensional problems and the results are presented as STL-files using implicit surface based geometry and marching cubes. It is demonstrated that the proposed game generates designs that have good performance for both the static and harmonic load cases and efficiently can avoid resonance at the frequencies of the harmonic loads.