The rapid growth of online grocery shopping requires recommendation systems that capture cyclical purchasing behavior and diverse user intents. Traditional item-level methods face scalability and accuracy challenges, motivating category-level recommendation as a more structured and practical alternative. We present GrocLM, a fine-tuned language model for grocery category recommendation in a real-world production environment. GrocLM employs a two-stage LoRA-based training strategy to encode cyclical purchasing patterns directly into model parameters, enabling more effective utilization of rebuying signals compared to prompt-based conditioning. To ensure valid and controllable outputs, we further introduce a trie-based constrained decoding mechanism over a predefined category space. Experiments on both proprietary production data and a public benchmark demonstrate that GrocLM consistently outperforms strong baselines. In a live production restocking task, GrocLM achieves a 7.5% relative improvement in cart-adds per impression while maintaining efficient inference by generating all categories jointly. These results highlight the effectiveness and practicality of integrating large language models into structured recommendation systems.