This article primarily aims to introduce high school students to the mystery of Lobachevsky geometry, one of the cornerstones of non-Euclidean geometries. Lobachevsky geometry, often known as hyperbolic geometry, differs from Euclidean geometry in several basic ways. The concepts and figures of Lobachevsky geometry can appear in different plane models, such as the Klein and Poincaré disk models. It further examines students' general attitudes and behaviors toward non-Euclidean geometries. Lobachevsky's geometry has helped expand students' horizons and enriched their critical thinking skills by challenging traditional Euclidean paradigms. This study is supported by a mixed-method approach utilizing quantitative and qualitative data. The mock exam results obtained from students during the educational process were compared, and the study was further supported by the positive feedback received from the participating students. The intriguing lessons on Lobachevsky geometry were conducted over 4 weeks, with weekly 2-hour geometry classes involving 12th-grade students at Stirling Schools in Erbil. Throughout the study, we observed significant improvements in students' ability to adopt, understand, and apply advanced geometric concepts. This article also discusses findings and implications that address gaps in the literature and considers the potential for curriculum updates to enhance the future of geometry education.