Self-driving laboratories (SDLs) are rapidly transforming research in chemistry and materials science to accelerate new discoveries. Mobile robot chemists (MRCs) play a pivotal role by autonomously navigating the lab to transport samples, effectively connecting synthesis, analysis, and characterisation equipment. The instruments within an SDL are typically designed or retrofitted to be accessed by both human and robotic chemists, ensuring operational flexibility and integration between manual and automated workflows. In many scenarios, human and robotic chemists may need to use the same equipment simultaneously. Currently, MRCs rely on simple LiDAR-based obstruction detection, which forces the robot to passively wait if a human is present. This lack of situational awareness leads to unnecessary delays and inefficient coordination in time-critical automated workflows in human-robot shared labs. To address this, we present an initial study of an embodied, AI-driven perception method that facilitates proactive human-robot interaction in shared-access scenarios. Our method features a hierarchical human intention prediction model that allows the robot to distinguish between preparatory actions (waiting) and transient interactions (accessing the instrument). Our results demonstrate that the proposed approach enhances efficiency by enabling proactive human-robot interaction, streamlining coordination, and potentially increasing the efficiency of autonomous scientific labs.