Lattice structure are innovative materials that leverage the interaction between the macroscale and microscale to optimize structural efficiency. The rigidity and load resistance at the macroscale are influenced by the shape of microscale unit cells, where proper design can lead to minimal material. Lattice structures are commonly constructed by repeating identical or similar unit cells, and lower-dimensional structural elements such as beams or shells are employed at the microscale to further optimize the stiffness-to-weight ratio. Unit cells for shell-based lattice structures can be defined either explicitly or implicitly. Explicit definitions use auxiliary parametric domains to construct a collection of patches in R^3 that produces the desired geometry, while implicit definitions employ level-set functions where the surface corresponds to the zero level-set. Examples of this second class, include triply periodic minimal surfaces (TPMS) expressed through combinations of trigonometric functions. Mechanical analysis typically involves homogenization, that adopts equivalent constitutive models. However, when there is not a clear scale separation, in order to increase accuracy, a full-scale analysis is necessary. For surfaces defined implicitly, a standard approach would require a conversion to an explicit representation to further construct a surface mesh. As an altarnative, in TraceFEM the implicit surface is embedded in a 3D structured grid and the equations are modified to project quantities of interest onto the surface. Basis functions remain in 3D, while stabilization is applied in each cell to avoid poorly conditioned stiffness matrices. In this work, the TraceFEM method is adopted to perform the linear elastic static analysis of shell-based TPMS lattice structures. The numerical implementation is carried out using QUGaR (Quadratures for Unfitted GeometRies), a recently released library that extends FEniCSx with support for unfitted finite element simulations.