Over the past decade, Max-pressure (MP) traffic signal control has evolved from a novel mathematical concept to a simple store-and-forward queuing model and has gained significant attention. However, the MP control in the past, which is based on traffic movements, has two problems. The first problem is the movement-based MP control aggregates the characteristics of lane groups, ignoring individual differences. The second problem is the movement-based MP control assumes that different movements are separate and do not block each other. To address these issues, this study proposes a lane-based MP control. This paper presents a series of numerical results comparing lane-based MP control with movement-based MP control at both an isolated intersection and a network comprising two intersections. The numerical results showed that lane-based MP control leads to a smaller number of queueing vehicles. At the isolated intersection, the number of queueing vehicles is reduced by up to 8.6%, while in the network with two intersections, the number of queueing vehicles decreases by up to 7.7%. This paper presents the proposed lane-based MP control also effectively handles intersections where movements are not strictly separate. By considering individual lanes and movements not strictly separate, this approach provides a more nuanced and efficient solution for traffic signal optimization.