Low-dose computed tomography (LDCT) imaging employed in lung cancer screening (LCS) programs is increasing in uptake worldwide. LCS programs herald a generational opportunity to simultaneously detect cancer and non-cancer-related early-stage lung disease. Yet these efforts are hampered by a shortage of radiologists to interpret scans at scale. Here, we present TANGERINE, a computationally frugal, open-source vision foundation model for volumetric LDCT analysis. Designed for broad accessibility and rapid adaptation, TANGERINE can be fine-tuned off the shelf for a wide range of disease-specific tasks with limited computational resources and training data. Relative to models trained from scratch, TANGERINE demonstrates fast convergence during fine-tuning, thereby requiring significantly fewer GPU hours, and displays strong label efficiency, achieving comparable or superior performance with a fraction of fine-tuning data. Pretrained using self-supervised learning on over 98,000 thoracic LDCTs, including the UK's largest LCS initiative to date and 27 public datasets, TANGERINE achieves state-of-the-art performance across 14 disease classification tasks, including lung cancer and multiple respiratory diseases, while generalising robustly across diverse clinical centres. By extending a masked autoencoder framework to 3D imaging, TANGERINE offers a scalable solution for LDCT analysis, departing from recent closed, resource-intensive models by combining architectural simplicity, public availability, and modest computational requirements. Its accessible, open-source lightweight design lays the foundation for rapid integration into next-generation medical imaging tools that could transform LCS initiatives, allowing them to pivot from a singular focus on lung cancer detection to comprehensive respiratory disease management in high-risk populations.