Advances in manufacturing such as 3d printing technologies made the investigation of stochastic lattices and other complex cellular materials a fast growing research field in both academia and industry. However, the possibilities to obtain lattice-filled high-performance structures from topology optimization are still limited due to numerical difficulties arising from manufacturing constraints on the design variables. After incorporation of these constraints into a standard minimum compliance problem, it is found to fall into the class of NP-hard mixed-integer programming problems, such that well-established topology optimization approaches including bi-directional structural optimization (BESO) and the optimality criteria method (OC) may not be applied directly to find a solution. To circumvent the limitations of the individual methods, we propose a combined BESO-OC method that updates the integer and continuous design variables simultaneously. We successfully apply the new method to compute stiffness-improved lattice-designs for an academic example as well as a real-world aircraft component. Thereby, the material behaviour of the stochastic lattice is described through a physics-augmented neural network formulation taking isotropic material symmetry into account.