Learning management systems (LMSs) are established tools in higher education, especially in the field of software engineering (SE). The onset of the COVID-19 pandemic further amplified the utilization of these systems, which necessitated their integration into educational curricula for both lecturers and students. However, adopting LMSs within SE education has presented distinctive challenges impeding their seamless incorporation into the courses. This paper aims to scrutinize the challenges and requirements encountered by professors, lecturers, and students in the domain of SE education when using LMSs. We conducted an empirical study that included (i) a survey with 47 professors/lecturers and 133 students, (ii) an analysis of the ensuing data, and (iii) 18 additional interviews conducted with professors and lecturers to delve into nuanced variations in viewpoints. The findings derived from our study reveal that the challenges and requirements pertaining to LMSs are rather specific depending on the scope and size of the respective courses. Nevertheless, many participants have a consensus on numerous challenges and requirements for improving certain features of LMSs in order to improve their usage in SE education. The findings are valuable for advancing research and development in the field of LMSs and provide guidance for lecturers in SE education.