This paper explores the lemmatization of multi-word expressions (MWEs) and proper names in Polish – tasks complicated by linguistic irregularities and historical factors. Instead of using rule-based methods, we apply a machine learning approach with fine-tuned plT5 and mT5 models. We trained and validated the models on enhanced gold-standard data from the 2019 PolEval task and evaluated the impact of additional fine-tuning on a silver-standard dataset derived from Wikipedia. Two setups were tested: one without context, and one using left-side context of the target MWE. Our best model achieved 86.23% AccCS (Accuracy Case-Sensitive), 89.43% AccCI (Accuracy Case-Insensitive), and a combined score of 88.79%, setting a new state-of-the-art for Polish MWE and named entity lemmatization, as confirmed by the PolEval maintainers. We also evaluated optimization and quantization techniques to reduce model size and inference time with minimal quality loss.