Recent advances in lifelong learning for convolutional neural networks have eliminated many of the hindrances to learning new classes in real time that exist among traditional deep learning models which are limited to being trained in an offline setting. These advanced continual learning algorithms, however, still assume a closed set of classes for training and cannot appropriately label novel or unknown samples at test time. We explored the synthesis of novelty detection techniques, also known as open set recognition, in deep neural networks, with recent continual learning strategies to enable lifelong learning models to identify and learn from novel unknown classes when presented in a continuous stream of data. We specifically show how open set recognition techniques are affected by incremental class learning strategies and how novelty detection performance can be recovered through a simple but unique classifier strategy. Finally, we establish the first known baselines for open set recognition on common incrementally learned computer vision datasets.