Sequence-dependent setup times (SDSTs) and delayed precedence (DP) occur commonly in various manufacturing settings. This study investigated the single machine scheduling problem with SDSTs and DP constraints arising in an amplifier assembly company. A mixed-integer linear programming model and a lean iterated greedy (LIG) algorithm is proposed to search for the best job sequence with minimum makespan. Based on the characteristic of delayed precedence constraints of the problem, the proposed LIG algorithm implements a straightforward but effective lean construction mechanism, which can keep the search process within the feasible solution space and quickly converge toward the (near-) global optimum. Computational results reveal that LIG significantly outperforms the state-of-the-art algorithm in terms of solution quality and computational efficiency. This study mainly contributes to providing a simple, effective, and efficient algorithm that can facilitate industrial applications and act as a new benchmark approach for future research.