Clinical electroencephalogram (EEG) reports encode domain-specific linguistic conventions that general-purpose language models (LMs) fail to capture. We introduce NeuroLex, a lightweight domain-adaptive language model trained purely on EEG report text from the Harvard Electroencephalography Database. Unlike existing biomedical LMs, NeuroLex is tailored to the linguistic and diagnostic characteristics of EEG reporting, enabling it to serve as both an independent textual model and a decoder backbone for multimodal EEG-language systems. Using span-corruption pretraining and instruction-style fine-tuning on report polishing, paragraph summarization, and terminology question answering, NeuroLex learns the syntax and reasoning patterns characteristic of EEG interpretation. Comprehensive evaluations show that it achieves lower perplexity, higher extraction and summarization accuracy, better label efficiency, and improved robustness to negation and factual hallucination compared with general models of the same scale. With an EEG-aware linguistic backbone, NeuroLex bridges biomedical text modeling and brain-computer interface applications, offering a foundation for interpretable and language-driven neural decoding.