While generative artificial intelligence has been used to design materials and structures for additive manufacturing, current techniques can only generate design parameters. However, not only design parameters but also additive manufacturing (AM) process parameters affect the mechanical properties of additively manufactured materials. To address this issue, we introduce an auxiliary classifier generative adversarial network (ACGAN)-based computational framework that generates both design and AM process parameters to fabricate lattice structures with target mechanical performance. The computational framework consists of two ACGAN models, including a generative model called InverseACGAN and a forward predictive model called ForwardACGAN. The generative model generates critical design parameters of the lattice structures, including line distance, layer height, and infill pattern, as well as AM process parameters, including print speed and print temperature, based on target mechanical properties (i.e., porosity and compressive modulus). The forward predictive model predicts the mechanical properties of the lattice structures generated by the generative model. The experimental results show that the porosity and compressive modulus of the lattice structures designed by ACGAN are in good agreement with the target porosity and compressive modulus. The average mean absolute percentage errors between target and actual porosity, and target and actual compressive modulus are 6.481% and 10.208%, respectively.