In this paper, we focus on the problem of whether efficient Lithuanian large language models (LLMs) can be achieved from Llama2 LLMs, which lack Lithuanian-specific components. Although the Llama2 architecture was previously successfully utilised to derive various regional LLMs, we propose and describe the first open Llama2 LLMs for the Lithuanian language (7 and 13 billion parameter versions), an accompanying question/answer (Q/A) dataset, and translations of popular language understanding benchmarks (Arc, Belebele, Hellaswag, MMLU, TruthfulQA, and Winogrande), which contribute to the standardisation of Lithuanian LLM evaluation. We empirically evaluate the proposed models by investigating their perplexity and performance in the translated language understanding benchmarks. The perplexity experiments show that it decreases consistently during pretraining, reflecting enhanced next-token prediction capabilities. Benchmarking the proposed LLMs against language understanding tasks reveals that high-quality pretraining datasets may be essential to achieve models that perform efficiently on these benchmarks. Comparison of the proposed LLMs with the latest open multilingual LLM shows that our model with 13 billion parameters is ranked 4th of 8 models in tasks such as Arc, Hellaswag, and Winogrande, but is generally outperformed in other tasks. These benchmarks allow us to hypothesise that from recent LLMs more efficient Lithuanian language models can be derived in the future. The complete realisations of the LLMs and other contributed components are available in the accompanying open repository https://huggingface.co/neurotechnology.