In this paper, we explore the capabilities of LLMs in capturing lexical-semantic knowledge from WordNet on the example of the LLaMA-2-7b model and test it on multiple lexical semantic tasks. As the outcome of our experiments, we present TaxoLLaMA, the “all-in-one” model for taxonomy-related tasks, lightweight due to 4-bit quantization and LoRA. TaxoLLaMA achieves 11 SOTA results, and 4 top-2 results out of 16 tasks on the Taxonomy Enrichment, Hypernym Discovery, Taxonomy Construction, and Lexical Entailment tasks. Moreover, it demonstrates a very strong zero-shot performance on Lexical Entailment and Taxonomy Construction with no fine-tuning. We also explore its hidden multilingual and domain adaptation capabilities with a little tuning or few-shot learning. All datasets, code, and pre-trained models are available online (code: https://github.com/VityaVitalich/TaxoLLaMA)