In this work, we explore the prediction of lexical complexity by combining supervised approaches and the use of large language models (LLMs). We first evaluate the impact of different prompting strategies (zero-shot, one-shot, and chain-of-thought) on the quality of the predictions, comparing the results with human annotations from the CompLex 2.0 corpus. Our results indicate that LLMs, and in particular gpt-4o, benefit from explicit instructions to better approximate human judgments, although some discrepancies remain. Moreover, a calibration approach to better align LLMs predictions and human judgements based on few manually annotated data appears as a promising solution to improve the reliability of the annotations in a supervised scenario.