We perform a search for galaxy-galaxy strong lens systems using a convolutional neural network (CNN) applied to imaging data from the first public data release of the DECam Local Volume Exploration Survey, which contains ~520 million astronomical sources covering ~4000 deg2 of the southern sky to a 5σ point-source depth of g = 24.3, r = 23.9, i = 23.3, and z = 22.8 mag. Following the methodology of similar searches using Dark Energy Camera data, we apply color and magnitude cuts to select a catalog of ~11 million extended astronomical sources. After scoring with our CNN, the highest-scoring 50,000 images were visually inspected and assigned a score on a scale from 0 (not a lens) to 3 (very probable lens). We present a list of 581 strong lens candidates, 562 of which are previously unreported. We categorize our candidates using their human-assigned scores, resulting in 55 Grade A candidates, 149 Grade B candidates, and 377 Grade C candidates. We additionally highlight eight potential quadruply lensed quasars from this sample. Due to the location of our search footprint in the northern Galactic cap (b > 10 deg) and southern celestial hemisphere (decl. < 0 deg), our candidate list has little overlap with other existing ground-based searches. Where our search footprint does overlap with other searches, we find a significant number of high-quality candidates that were previously unidentified, indicating a degree of orthogonality in our methodology. We report properties of our candidates including apparent magnitude and Einstein radius estimated from the image separation.