The rise of additive manufacturing, particularly laser powder bed fusion, has enabled new degrees of freedom in terms of design and functionality. Notably high-performance industries such as the medical, automotive, and aerospace industries are on the edge of broad industrial application. However, the quality standards required for these industries are not yet entirely met. Process-related temperature-induced residual stresses within the component can lead to warpage and deformations causing rejects. Support structures are a vital counter measure to absorb these residual stresses and ensure the required print quality. While the current industrial standard for support structure generation mainly focuses on geometrical boundary conditions, this study presents a simulation-based approach taking into account residual stresses. The proposed approach determines the stress distribution during the process from a thermomechanical finite element process simulation and uses these results for the allocation of topology-optimized stackable unit cells. To assure a reliable connection to the component while offering easy removability of the support, different connection support structures in the interface area were tested and integrated in the proposed approach. The result is a robust tailored lattice support structure minimizing residual stresses to achieve high component quality, while focusing on cost-efficiency factors such as minimal material usage, easy support removability, and numerical efficiency. Finally, the proposed approach was tested on a demonstrator part printed from AlSi10Mg.