Communicating complex scientific findings to non-experts remains a major challenge in fields like psychology, where research is often presented in highly technical language. One effective way to improve accessibility, for non-experts, is through plain language summaries, which summarize key insights into simple and understandable terms. However, the limited number of institutions that produce lay summaries typically relies on psychology experts to create them manually – an approach that ensures high quality but requires significant expertise, time, and effort. In this paper, we introduce the KLARpsy App, a system designed to support psychology experts in creating plain language summaries of psychological meta-analyses using Large Language Models (LLM). Our system generates initial draft summaries based on a 37-criterion guideline developed to ensure clarity for non-experts. All summaries produced through the system are manually validated and edited by KLARpsy authors to ensure factual correctness and readability. We demonstrate how the system integrates LLM-generated content into an expert-in-the-loop workflow. The automatic evaluation showed a mean semantic-similarity score of 0.73 against expert-written summaries, and human evaluation on a 5-point Likert scale averaged above 3 (higher is better), indicate that the generated drafts are of high quality. The application and code are open source.