Trust plays a pivotal role in Lecturer-Student-Collaboration, encompassing teaching and research aspects. The advent of Large Language Models (LLMs) in platforms like Open AI's ChatGPT, coupled with their cost-effectiveness and high-quality results, has led to their rapid adoption among university students. However, discerning genuine student input from LLM-generated output poses a challenge for lecturers. This dilemma jeopardizes the trust relationship between lecturers and students, potentially impacting university downstream activities, particularly collaborative research initiatives. Despite attempts to establish guidelines for student LLM use, a clear framework mutually beneficial for lecturers and students in higher education remains elusive. This study addresses the research question: How does the use of LLMs by students impact Informational and Procedural Justice, influencing Team Trust and Expected Team Performance? Methodically, we applied a quantitative construct-based survey, evaluated using techniques of Structural Equation Modelling (PLS- SEM) to examine potential relationships among these constructs. Our findings based on 23 valid respondents from Ndejje University indicate that lecturers are less concerned about the fairness of LLM use per se but are more focused on the transparency of student utilization, which significantly influences Team Trust positively. This research contributes to the global discourse on integrating and regulating LLMs and subsequent models in education. We propose that guidelines should support LLM use while enforcing transparency in Lecturer-Student- Collaboration to foster Team Trust and Performance. The study contributes valuable insights for shaping policies enabling ethical and transparent LLMs usage in education to ensure effectiveness of collaborative learning environments.