Complex Word Identification (CWI) is an essential step in the lexical simplification task and has recently become a task on its own. Some variations of this binary classification task have emerged, such as lexical complexity prediction (LCP) and complexity evaluation of multi-word expressions (MWE). Large language models (LLMs) recently became popular in the Natural Language Processing community because of their versatility and capability to solve unseen tasks in zero/few-shot settings. Our work investigates LLM usage, specifically open-source models such as Llama 2, Llama 3, and Vicuna v1.5, and closed-source, such as ChatGPT-3.5-turbo and GPT-4o, in the CWI, LCP, and MWE settings. We evaluate zero-shot, few-shot, and fine-tuning settings and show that LLMs struggle in certain conditions or achieve comparable results against existing methods. In addition, we provide some views on meta-learning combined with prompt learning. In the end, we conclude that the current state of LLMs cannot or barely outperform existing methods, which are usually much smaller.