Dialects exhibit a substantial degree of variation due to the lack of a standard orthography. At the same time, the ability of Large Language Models (LLMs) to process dialects remains largely understudied. To address this gap, we use Bavarian as a case study and investigate the lexical dialect understanding capability of LLMs by examining how well they recognize and translate dialectal terms across different parts-of-speech. To this end, we introduce DiaLemma, a novel annotation framework for creating dialect variation dictionaries from monolingual data only, and use it to compile a ground truth dataset consisting of 100K human-annotated German-Bavarian word pairs. We evaluate how well nine state-of-the-art LLMs can judge Bavarian terms as dialect translations, inflected variants, or unrelated forms of a given German lemma. Our results show that LLMs perform best on nouns and lexically similar word pairs, and struggle most in distinguishing between direct translations and inflected variants. Interestingly, providing additional context in the form of example usages improves the translation performance, but reduces their ability to recognize dialect variants. This study highlights the limitations of LLMs in dealing with orthographic dialect variation and emphasizes the need for future work on adapting LLMs to dialects.