Lifelong graph learning deals with the problem of continually adapting graph neural network (GNN) models to changes in evolving graphs. We address two critical challenges of lifelong graph learning in this work: dealing with new classes and tackling imbalanced class distributions. The combination of these two challenges is particularly relevant since newly emerging classes typically resemble only a tiny fraction of the data, adding to the already skewed class distribution. We make several contributions: First, we show that the amount of unlabeled data does not influence the results, which is an essential prerequisite for lifelong learning on a sequence of tasks. Second, we experiment with different label rates and show that our methods can perform well with only a tiny fraction of annotated nodes. Third, we propose the gDOC method to detect new classes under the constraint of having an imbalanced class distribution. The critical ingredient is a weighted binary cross-entropy loss function to account for the class imbalance. Moreover, we demonstrate combinations of gDOC with various base GNN models such as GraphSAGE, Simplified Graph Convolution, and Graph Attention Networks. Lastly, our k-neighborhood time difference measure provably normalizes the temporal changes across different graph datasets. With extensive experimentation, we find that the proposed gDOC method is consistently better than a naive adaption of DOC to graphs. Specifically, in experiments using the smallest history size, the out-of-distribution detection score of gDOC is 0.09 compared to 0.01 for DOC. Furthermore, gDOC achieves an Open-F1 score, a combined measure of in-distribution classification and out-of-distribution detection, of 0.33 compared to 0.25 of DOC (32% increase).