Although large language models (LLMs) have transformed our expectations of modern language technologies, concerns over data privacy often restrict the use of commercially available LLMs hosted outside of EU jurisdictions. This limits their application in governmental, defence, and other data-sensitive sectors. In this work, we evaluate the extent to which locally deployable open-weight LLMs support lesser-spoken languages such as Lithuanian, Latvian, and Estonian. We examine various size and precision variants of the top-performing multilingual open-weight models, Llama~3, Gemma~2, Phi, and NeMo, on machine translation, multiple-choice question answering, and free-form text generation. The results indicate that while certain models like Gemma~2 perform close to the top commercially available models, many LLMs struggle with these languages. Most surprisingly, however, we find that these models, while showing close to state-of-the-art translation performance, are still prone to lexical hallucinations with errors in at least 1 in 20 words for all open-weight multilingual LLMs.