We present the winning entry to the Multilingual Lexical Normalization (MultiLexNorm) shared task at W-NUT 2021 (van der Goot et al., 2021a), which evaluates lexical-normalization systems on 12 social media datasets in 11 languages. We base our solution on a pre-trained byte-level language model, ByT5 (Xue et al., 2021a), which we further pre-train on synthetic data and then fine-tune on authentic normalization data. Our system achieves the best performance by a wide margin in intrinsic evaluation, and also the best performance in extrinsic evaluation through dependency parsing. The source code is released at https://github.com/ufal/multilexnorm2021 and the fine-tuned models at https://huggingface.co/ufal.