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INTRODUCTION Deep learning (DL) models that use medical images to predict clinical outcomes are poised for clinical translation. For tumors that reside in organs that move, however, the impact of motion (i.e. degenerated object appearance or blur) on DL model accuracy remains unclear. We examine the impact of tumor motion on an image-based DL framework that predicts local failure risk after lung stereotactic body radiotherapy (SBRT). METHODS We input pre-therapy free breathing (FB) CT images from 849 patients treated with lung SBRT into a multi-task deep neural network to generate an image fingerprint signature (or DL score) that predicts time-to-event local failure outcomes. The network includes a convolutional neural network encoder for extracting imaging features and building a task-specific fingerprint, a decoder for estimating handcrafted radiomic features, and a task-specific network for generating image signature for radiotherapy outcome prediction. The impact of tumor motion on the DL scores was then examined for a holdout set of 468 images from 39 patients comprising: (1) FB CT, (2) four-dimensional (4D) CT, and (3) maximum-intensity projection (MIP) images. Tumor motion was estimated using a 3D vector of the maximum distance travelled and its association with DL score variance was assessed by linear regression. FINDINGS The variance and amplitude in 4D CT image-derived DL scores were associated with tumor motion (R2 = 0.48 and 0.46, respectively). Specifically, DL score variance was deterministic and represented by sinusoidal undulations in phase with the respiratory cycle. DL scores, but not tumor volumes, peaked near end-exhalation. The mean of the scores derived from 4D CT images and the score obtained from FB CT images were highly associated (Pearson r = 0.99). MIP-derived DL scores were significantly higher than 4D- or FB-derived risk scores (p < 0.0001). INTERPRETATION We show that an image-based DL risk score derived from a series of 4D CT images varies in a deterministic, sinusoidal trajectory in phase with the respiratory cycle. These results indicate that deep learning models of tumors in motion can be robust to fluctuations in object appearance due to movement and can guide standardization processes in the clinical translation of DL models for patients with lung cancer. This article is protected by copyright. All rights reserved.