Grammatical Error Correction (GEC) tasks typically rely on high-quality corpora, and data augmentation through synthesized data has been widely applied in rich-resource languages. However, normal data augmentation approaches are difficult to directly apply to the low-resource Lao due to its unique tonal and specific grammatical characteristics. To address this issue, we for the first time annotate and release a high-quality Lao-specific grammatical error correction corpus, named LaoGEC, which is first generated by an automatic speech recognition model and then manually annotated by Laotians. Meanwhile, we propose a linguistic error-aware data augmentation method based on Multilingual Large Language Models (MLLMs) to improve Lao grammatical error correction. First, we extract phonological and grammatical error-aware sets based on our LaoGEC corpus and human verification. Next, we exploit two linguistic error-aware sets to constrain MLLMs, thus generating a diverse yet comprehensive synthetic corpus to mimic real-world Lao error distribution. Finally, our linguistic error-aware synthetic corpus is integrated with the LaoGEC data to optimize both traditional and MLLMs-based GEC models. Experiments on our benchmark dataset indicate that our synthetic corpus can consistently improve the correction performance of all strong baseline models, achieving state-of-the-art results. Detailed analysis shows that the phonological and grammatical error sets are extremely useful and can complement each other to ensure the diversity and affinity of our synthetic corpus. In-depth comparative experiments indicate that high-quality synthetic corpora can effectively enhance the learning ability of all GEC models.