A vacuum lifter is widely used to hold and pick up large, heavy, and flat objects. Conventionally, when using a vacuum lifter, a human worker watches the state of a running vacuum lifter and adjusts the object's pose to maintain balance. In this work, we propose using a dual-arm robot to replace the human workers and develop planning and control methods for a dual-arm robot to raise a heavy plate with the help of a vacuum lifter. The methods help the robot determine its actions by considering the vacuum lifer's suction position and suction force limits. The essence of the methods is two-fold. First, we build a Manipulation State Graph (MSG) to store the weighted logical relations of various plate contact states and robot/vacuum lifter configurations, and search the graph to plan efficient and low-cost robot manipulation sequences. Second, we develop a velocity-based impedance controller to coordinate the robot and the vacuum lifter when lifting an object. With its help, a robot can follow the vacuum lifter's motion and realize compliant robot-vacuum lifter collaboration. The proposed planning and control methods are investigated using real-world experiments. The results show that a robot can effectively and flexibly work together with a vacuum lifter to manipulate large and heavy plate-like objects with the methods' support.