Lexically constrained neural machine translation (NMT) draws much industrial attention for its practical usage in specific domains. However, current autoregressive approaches suffer from high latency. In this paper, we focus on non-autoregressive translation (NAT) for this problem for its efficiency advantage. We identify that current constrained NAT models, which are based on iterative editing, do not handle low-frequency constraints well. To this end, we propose a plug-in algorithm for this line of work, i.e., Aligned Constrained Training (ACT), which alleviates this problem by familiarizing the model with the source-side context of the constraints. Experiments on the general and domain datasets show that our model improves over the backbone constrained NAT model in constraint preservation and translation quality, especially for rare constraints.