This study investigates the issues of data privacy protection, digital rights, and compliance in Moodle-based learning management systems (LMS) in the Nigerian universities with respect to complying with the Nigeria Data Protection Act (NDPA, 2023) and the European Union's General Data Protection Regulation (GDPR). A mixed-method design was employed involving structured questions of 250 students, lecturers, and administrators, alongside in-depth case studies at the University of Lagos and the National Open University of Nigeria. Moodle configuration audits were carried out as well, and data were analysed by descriptive statistics and coding interview themes. Findings reveal significant obstacles, such as limited implementation of Data Protection Impact Assessments (22% compliance), the lack of Data Protection Officers in 73% of institutions, and deficient subject-consent strategies. These gaps have been highlighted based on empirical evidence, as one lecturer remarked at the University of Lagos, "our institution has no policy of how students are informed about the way their data is kept." Privacy features include role-based access control, data anonymisation, and audit logs, which have been underused by Moodle even though the privacy feature has several available plugins. Relative to European, Asian, and South African experience, it is evident that Nigeria's formal compliance is still low. Whereas NOUN has shown 100 percent uptime since 2018, privacy workflows need to be improved. The study recommends automation of the DPIAs, the implementation of DPOs, and the creation of NDPA-GDPR hybrid systems of compliance to better protect the subjects' digital rights.