Lexical relation refers to the way words are related within a language. Prior work has demonstrated that pretrained language models (PLMs) can effectively mine lexical relations between word pairs. However, they overlook the potential of graph structures composed of lexical relations, which can be integrated with the semantic knowledge of PLMs. In this work, we propose a parameter-efficient fine-tuning method through graph context, which integrates graph features and semantic representations for lexical relation classification (LRC) and lexical entailment (LE) tasks. Our experiments show that graph features can help PLMs better understand more complex lexical relations, establishing a new state-of-the-art for LRC and LE. Finally, we perform an error analysis, identifying the bottlenecks of language models in lexical relation mining tasks and providing insights for future improvements.