Despite rapid advances in large language models (LLMs), their linguistic abilities in low-resource and morphologically rich languages are still not well understood due to limited annotated resources and the absence of standardized evaluation frameworks. This paper presents LLM Probe, a lexicon-based assessment framework designed to systematically evaluate the linguistic skills of LLMs in low-resource language environments. The framework analyzes models across four areas of language understanding: lexical alignment, part-of-speech recognition, morphosyntactic probing, and translation accuracy. To illustrate the framework, we create a manually annotated benchmark dataset using a low-resource Semitic language as a case study. The dataset comprises bilingual lexicons with linguistic annotations, including part-of-speech tags, grammatical gender, and morphosyntactic features, which demonstrate high inter-annotator agreement to ensure reliable annotations. We test a variety of models, including causal language models and sequence-to-sequence architectures. The results reveal notable differences in performance across various linguistic tasks: sequence-to-sequence models generally excel in morphosyntactic analysis and translation quality, whereas causal models demonstrate strong performance in lexical alignment but exhibit weaker translation accuracy. Our results emphasize the need for linguistically grounded evaluation to better understand LLM limitations in low-resource settings. We release LLM Probe and the accompanying benchmark dataset as open-source tools to promote reproducible benchmarking and to support the development of more inclusive multilingual language technologies.