Vehicle incidents on roads result in lane closure and severe traffic congestion, and the frequent mandatory lane changes of the upstream vehicles generate capacity drops ahead of the incidents, which further increase road congestion. With the development of connected vehicles, vehicle incidents can be detected by individual vehicles, and immediate driving assistance can be provided to help them pass the incidents efficiently. This paper proposes a distributed lane-changing assistant (DLCA) system with connected vehicles to advise individual vehicles with the optimal lanes to pass incidents with smaller delays. The system introduces connected vehicles to detect the location and the lane closure information of an incident and broadcast the information to the upstream connected vehicles. To determine the optimal lane for each connected vehicle, a speed index is defined for each lane based on the incident information and the downstream connected vehicle dynamics. The DLCA system is evaluated with a microscopic traffic simulator, INTEGRATION, to illustrate its benefits in improving the performance of individual vehicles and mitigating road congestion. A sensitivity analysis of market penetration rates and demand levels of connected vehicles is also conducted in this paper. The results indicate that the DLCA system can reduce the delay by about 22.1% for the connected vehicles, and it has higher benefits on improving the performance of the entire road at higher market penetration rates. In addition, there exists an optimal demand level to maximize the benefits of the system.