Lobed mixer wind turbines have the lobed mixer added around the turbine, enhancing the wind power compared to conventional wind turbines. This article aims to design a bare lobed mixer that satisfies the multi-objectives of maximizing average throat (where the turbine blades are fixed) velocity uavg and minimizing drag coefficient Cd. The objectives are set considering that a bare enclosure with a higher uavg will produce higher power output when the turbine is included. Numerical simulations were performed to understand the flow characteristics of the non-lobed and lobed enclosure using ansys fluent. The lobed mixer angle was varied using a one factor at a time (OFAT) approach, and the angle with the highest uavg/Cd was found. Then, by fixing the lobed mixer angle, multi-objective gray relation analysis (GRA) was used to optimize the lobed mixer’s three geometrical parameters, such as the number of lobes, lobe width, and lobe height simultaneously. The GRA results show that lobe height is the most significant parameter affecting throat velocity and drag coefficient, and the optimum combination which fulfills both objectives were found. The most significant lobe height was further analyzed to improve uavg using the OFAT approach. Then in the optimized enclosure, the plug/center body was included at the axis, and the performance of two different plug geometries was compared. NACA 0024 was found to be better plug cross section. Thus, the proposed design of lobed enclosure helps to enhance the average velocity as 1.76 times the freestream velocity and reduce the drag coefficient by 5.43% than the case without lobes. Hence lobed mixer is a better option to use as an enclosure, especially to reduce the drag forces.