Lean manufacturing principles are being increasingly employed in off-site construction (OSC) with the primary objective of reducing waste and improving production efficiency. This is performed using several tools and technologies largely influenced by the concept of Industry 4.0 (I4.0) that sets fundamental design principles for technological development. However, the recent introduction of the concept of Industry 5.0 (I5.0) extends the I4.0 focus toward wider economic, social, and environmental implications. This study aims to evaluate extant literature employing lean tools and concepts in OSC toward the realization of I4.0 and I5.0 design principles, identifying key research themes and gaps and suggesting future directions. A mixed-method review was employed to first identify highly relevant literature using a bibliometric search. The identified references were then analyzed using qualitative content analysis through the lens of I4.0 and I5.0. Results highlight several interactions between identified lean-OSC tools and concepts and I4.0 and I5.0 design principles, signifying the power of these tools/concepts in meeting multiple industry objectives. The review also identifies a significant overlap between the resilience principle in I5.0 and many of the I4.0 principles, emphasizing resilience as an integrative concept of technological principles. Finally, several research gaps relating to the social and environmental aspects of lean-OSC research were identified, including research on mental health, assistive technologies, and design for end-of-life.