Background: Accurate forecasting of lung tumor motion is essential for precise dose delivery in proton therapy. While current markerless methods mostly rely on deep learning, transformer-based architectures remain unexplored in this domain, despite their proven performance in trajectory forecasting. Purpose: This work introduces a markerless forecasting approach for lung tumor motion using Vision Transformers (ViT). Two training strategies are evaluated under clinically realistic constraints: a patient-specific (PS) approach that learns individualized motion patterns, and a multi-patient (MP) model designed for generalization. The comparison explicitly accounts for the limited number of images that can be generated between planning and treatment sessions. Methods: Digitally reconstructed radiographs (DRRs) derived from planning 4DCT scans of 31 patients were used to train the MP model; a 32nd patient was held out for evaluation. PS models were trained using only the target patient's planning data. Both models used 16 DRRs per input and predicted tumor motion over a 1-second horizon. Performance was assessed using Average Displacement Error (ADE) and Final Displacement Error (FDE), on both planning (T1) and treatment (T2) data. Results: On T1 data, PS models outperformed MP models across all training set sizes, especially with larger datasets (up to 25,000 DRRs, p < 0.05). However, MP models demonstrated stronger robustness to inter-fractional anatomical variability and achieved comparable performance on T2 data without retraining. Conclusions: This is the first study to apply ViT architectures to markerless tumor motion forecasting. While PS models achieve higher precision, MP models offer robust out-of-the-box performance, well-suited for time-constrained clinical settings.