Structures made of triply-periodic minimal surface (TPMS) lattices are gaining attention due to their attractive properties for combined mechanical and transport applications, and because TPMS lattices do not require internal supports for additive manufacturing due to their minimal-surface property. Current topology optimization (TO) techniques for TPMS lattices focus on the compliance minimization problem. While structural stiffness is an important requirement in many situations, it does not address material failure modes that are often associated with stress. Incorporating these requirements in the TO is essential to realize the application of TPMS lattices in demanding applications such as orthopedic implants. In this work, we present a method for the TO of structures made of sheet-network TPMS lattices. The cornerstone of our method is the formulation of surrogate models of the stress field in a unit cell of the TPMS as a function of applied external tractions, base material properties, and surface thickness. By exploiting the symmetries of the unit cell, we develop surrogates that can readily and efficiently predict desired values of stress invariants, such as the von Mises stress. Using these surrogates, we formulate a multi-scale TO technique that simultaneously determines the shape and topology of the macro structure and the thickness field for the TPMS lattice. The TO is performed using continuous solid elements whose mechanical properties are obtained via numerical homogenization. The stresses resulting from the analysis of the macro structure are subsequently used as inputs to the off-line stress surrogates to predict the largest TPMS unit cell stress at each point; and aggregation techniques commonly used in stress-constrained TO techniques are employed to produce a single constraint on the largest unit cell stress in the structure. The proposed method is demonstrated by application to well-known benchmarks in stress-based TO, such as the L-bracket problem.