Static mixers play a vital role in industrial applications such as polymer processing, where they enhance flow homogenization in highly viscous fluids to achieve a more uniform distribution of material or temperature. These mixers consist of specially designed stationary elements installed inside a tube, which manipulate the flow to facilitate efficient mixing and homogenization of temperature and material [1]. In this contribution, we report on the numerical design optimization of static mixers. An essential aspect of our design method is the integration of isogeometric shape optimization with lattice structures. These lattice structures are generated using spline-based functional composition, a concept originally introduced in [2]. The overall geometry is constructed from microtiles embedded within a volumetric spline - referred to as the macro shape - that defines the external form. By confining the design space to the design parameters of the microtiles and the macro shape, we maintain a low-dimensional parameter space, which facilitates the optimization process, while still offering a wide variety of achievable geometries. Our motivation for utilizing isogeometric analysis (IGA) lies in its use of spline-based geometries, which significantly reduces the time-consuming and computationally intensive processes of geometry preparation and meshing. For the optimization process, we employ a gradient-based optimization algorithm. Given the large number of design variables addressing both the microtiles and the macro shape, the use of adjoint methods becomes essential for efficient gradient computation. They enable us to handle the complexity of the design space without prohibitive computational costs. In this contribution, we will detail the developed method and demonstrate its capabilities through a test case.