The emerging urban air mobility (UAM) concept relies on distributed electric propulsion systems, where complex aerodynamic interactions among multiple rotors and lifting surfaces critically influence overall performance. This study presents a comprehensive mid-fidelity numerical analysis of the NASA lift+cruise vertical take-off and landing (VTOL) UAM concept aircraft, focusing on rotor-wing-rotor aerodynamic interactions during both hover and transition flight phases. The open-source vortex-based solver DUST [1] is employed to efficiently simulate the three-dimensional flow field, capturing wake evolution and mutual interference effects between lifting rotors and the wing. Numerical simulations are systematically performed to quantify the interactional aerodynamic phenomena and their impact on wing loading and rear rotor efficiency. Validation against high-fidelity CFD results from references [2,3] demonstrates good agreement, confirming the reliability of the mid-fidelity approach. Under hover conditions, wake interactions among the lifting rotors significantly alter the flow field at their tip regions, while the strong downwash streams induce substantial negative lift on the wing, creating a download penalty that must be compensated by increased rotor thrust. During transition conditions, the rear lifting rotors operate in the wake of upstream lifting rotors, resulting in reduced thrust efficiency and increased unsteady loading. These findings elucidate the complex coupling mechanisms in distributed propulsion UAM configurations and provide quantitative insights essential for performance prediction and design optimization.