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A robot cannot lift up an object if it is not feasible to do so. However, in most research on robot lifting, "feasibility" is usually presumed to exist a priori. This paper proposes a three-step method for a humanoid robot to reason about the feasibility of lifting a heavy box with physical properties that are unknown to the robot. Since feasibility of lifting is directly related to the physical properties of the box, we first discretize a range for the unknown values of parameters describing these properties and tabulate all valid optimal quasi-static lifting trajectories generated by simulations over all combinations of indices. Second, a physical-interaction-based algorithm is introduced to identify the robust gripping position and physical parameters corresponding to the box. During this process, the stability and safety of the robot are ensured. On the basis of the above two steps, a third step of mapping operation is carried out to best match the estimated parameters to the indices in the table. The matched indices are then queried to determine whether a valid trajectory exists. If so, the lifting motion is feasible; otherwise, the robot decides that the task is beyond its capability. Our method efficiently evaluates the feasibility of a lifting task through simple interactions between the robot and the box, while simultaneously obtaining the desired safe and stable trajectory. We successfully demonstrated the proposed method using a NAO humanoid robot.