Lexically-constrained NMT (LNMT) aims to incorporate user-provided terminology into translations. Despite its practical advantages, existing work has not evaluated LNMT models under challenging real-world conditions. In this paper, we focus on two important but understudied issues that lie in the current evaluation process of LNMT studies. The model needs to cope with challenging lexical constraints that are “homographs” or “unseen” during training. To this end, we first design a homograph disambiguation module to differentiate the meanings of homographs. Moreover, we propose PLUMCOT which integrates contextually rich information about unseen lexical constraints from pre-trained language models and strengthens a copy mechanism of the pointer network via direct supervision of a copying score. We also release HOLLY, an evaluation benchmark for assessing the ability of model to cope with “homographic” and “unseen” lexical constraints. Experiments on HOLLY and the previous test setup show the effectiveness of our method. The effects of PLUMCOT are shown to be remarkable in “unseen” constraints. Our dataset is available at https://github.com/papago-lab/HOLLY-benchmark.