The effective mechanical properties of lattice structures can be tailored by designing their underlying geometries. This enables achieving mechanical properties that are not easily achievable in conventional materials, such as negative Poisson’s ratios (i.e., auxeticity) and negative thermal expansion coefficients. As a result, the modeling and design of lattice structures have attracted increasing attention in recent years. In addition to analytical methods and numerical simulations, data-driven machine learning (ML) approaches have been increasingly used to solve relevant forward and inverse problems. However, the performance of ML models critically depends on the amount and quality of the available dataset. In most existing studies, training datasets are generated using high-throughput finite element simulations. For lattice structures composed of periodically connected struts, these simulations are usually based on beam elements and hence are computationally efficient. However, the simplification in beam theory and the improper treatment of strut joints may lead to low accuracy, especially for structures with low aspect-ratio struts. As a consequence, ML models trained only on low-fidelity data may show poor predictive performance. Solid element-based simulations provide higher accuracy by fully resolving the geometry. However, they are significantly more computationally expensive. In this contribution, we propose a multi-fidelity data-driven framework for constructing accurate ML-based property-prediction models for representative lattice structures. The approach leverages a large set of low-fidelity data together with a limited amount of high-fidelity data through transfer learning. First, a base ML model is trained using the low-fidelity dataset. Subsequently, a refinement model is trained on high-fidelity data to correct the predictions of the base model. The integrated multi-fidelity ML model achieves high accuracy and efficiency in predicting the effective properties of lattice structures. The proposed transfer learning framework opens new possibilities for ML-based modeling and design of lattice and other microstructured materials.