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In this paper, we propose and describe the first open Llama2 large language models (LLMs) for the Lithuanian language, including an accompanying question/answer (Q/A) dataset and translations of popular LLM benchmarks. We provide a brief review of open regional LLMs and detailed information on the proposed LLMs and their training process. We also conduct an empirical evaluation, comparing the perplexities of the proposed LLMs with those of other modern open LLMs. In addition, benchmarking the proposed LLMs against language understanding tasks reveals that high-quality pretraining datasets may be essential for achieving models that perform efficiently on these benchmarks. The full realisations of the described LLMs are available in the accompanying open repository~\url{https://huggingface.co/neurotechnology}.