This paper presents a novel Topological Machine Learning (TML) framework aimed at improving the classification of lung lesions in CT scans. The approach integrates topological data analysis with machine learning, leveraging persistent homology to derive a set of robust topological descriptors–including functional, vector-based, and image-based features. These descriptors represent the intrinsic shape and structure of lung lesions at multiple scales and, once properly converted into numerical feature vectors, are suitable for use in various classification algorithms. The framework is evaluated on the publicly available IQ-OTH/NCCD dataset, showing high classification accuracy and consistent performance across lesion types. These results demonstrate the effectiveness of TML –and topology more broadly–in extracting meaningful patterns from complex medical imaging data while maintaining interpretability and data efficiency. The proposed methodology offers a promising alternative to conventional radiomics or deep learning methods, especially in scenarios where model transparency, limited training data, and generalization are critical for clinical decision-making and diagnostics.