Lane-Change (LC) maneuvers are deemed to jeopardize traffic safety, mobility, and sustainability. Cooperative Lane-Change (CLC) solves this problem by accelerating the LC process. This research proposes an optimal control based CLC controller. It bears the following features: i) with the faster completion of a CLC maneuver by making space and changing lane at the same time; ii) with less speed oscillation perturbations on traffic. To make space and change lane at the same time, a formulation method in the relative spatial domain is proposed. In this method, the conventional longitudinal and lateral coupled nonlinear avoidance constraints are linearized into a relative longitudinal distance fixed lateral-only avoidance constraint. Evaluations indicate that the proposed method enhances the completion efficiency of CLC by 15.67%, reduce traffic emission by 0.24%, reduce fuel consumption by 0.36%, and improve traffic stability by 47.9%.