Legal Prompt Engineering (LPE) or Legal Prompting is a process to guide and assist a large language model (LLM) with performing a natural legal language processing (NLLP) skill. Our goal is to use LPE with LLMs over long legal documents for the Legal Judgement Prediction (LJP) task. We investigate the performance of zero-shot LPE for given facts in case-texts from the European Court of Human Rights (in English) and the Federal Supreme Court of Switzerland (in German, French and Italian). Our results show that zero-shot LPE is better compared to the baselines, but it still falls short compared to current state of the art supervised approaches. Nevertheless, the results are important, since there was 1) no explicit domain-specific data used - so we show that the transfer to the legal domain is possible for general-purpose LLMs, and 2) the LLMs where directly applied without any further training or fine-tuning - which in turn saves immensely in terms of additional computational costs.