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. 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. 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 our design space to the parameters of both the microtiles and the macro shape, we maintain a low-dimensional design space that influences both the micro- and macro-scale. 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. To quantify the mixing quality we introduce a novel cost function, which borrows concepts from the Shannon entropy. In this contribution, we will detail the developed method and demonstrate its capabilities using a representative test case, with particular emphasis on how geometric modifications at both the micro- and macro-scale affect the value of the cost function.