COVID-19 greatly increased the online delivery of higher education. But one limitation of online learning is that students often struggle to stay engaged while watching online lectures. We examined whether including an instructor's face in lecture videos (instructor visibility) enhances student engagement or learning. In two preregistered experiments, we found that instructor visibility in lecture videos did not affect either engagement or learning overall. However, participants reported higher engagement when they watched a video that aligned with their preference for instructor visibility. For example, participants who favored videos with the instructor visible reported greater engagement with such videos compared to those without the instructor, and vice versa. Additionally, we examined the effects of playback speed on engagement and learning. Our results suggest that speeded playing did not impact engagement but resulted in better learning efficiency. Lastly, using GPT, we explored participants' open-ended responses to understand their preference for video lectures.