The Mirror one Lower (LM1) is part of the in-vessel quasi-optical beam propagation system for the ITER Electro Cyclotron (EC) Upper Launcher (UL), where eight beams are reflected through four mirrors during its passage to the plasma. The mirrors are grouped into two rows of four beams each and the mirror LM1 refers to a four mirror set. High power millimeter (mm) waves are generated by the gyrotrons and delivered to the in-vessel components via corrugated wave-guides. The design of the LM1 shall guarantee the optimal propagation of the beams during their transmission through the optical system taking into consideration 1) the shape of the reflecting surfaces, 2) loads coming from the beams themselves, the plasma and nuclear reactions as well as off-normal events and 3) the port plug space restrictions. This paper reports the Ohmic loss assessment at LM1 as function of frequency, surface roughness and resistivity using the most suitable material and the power input (1.31 MW at 170 GHz). It describes the design investigation of the cooling solutions for the normal scenario via computational fluid dynamic analyses, based on the ITER Primary Heat Transfer System (PHTS) cooling boundary conditions, needed to remove similar to 20 kW of power deposition on the mirror surface. Finite element analyses are performed to guide the design choices in an effort to minimize the maximum mirror surface temperature and thus diminishing the deformation of the reflecting surfaces. The conclusion of this study will provide a feasible design solution for the LM1 and Upper Mirror 1 (UM1).