Prospects of $Y_2O_3$ have been more extended as a great promising and creditable material for optical, electronic and mechanical purposes. $Y_2O_3$ has been more observed as a fine ceramic which has great material properties: high light transparency, excellent thermal resistance and chemical inertness. But in terms of effective application of $Y_2O_3$, its hard and brittle nature needs to be overcome during the surface machining process. Therefore, the surface machining control of $Y_2O_3$ should be conducted carefully. The evaluation for stable and continuous machining should also be investigated in various industrial fields as there are only limited studies on the subject. The lapping process with in-process electrolytic dressing (IED) is widely used for surface machining of hard and brittle materials. In this study, $Y_2O_3$ surface machinability was evaluated by using the ultra-precision lapping process with IED method by changing three major variables: applied force, wheel speed and machining time. The most suitable value of Ra 92nm surface roughness was acquired with smooth surface quality from the following machining condition: 7kg of applied force, 60rpm of wheel speed and 30minutes of machining time. After the lapping process, the machining tendency and surface characteristics were analyzed with fracture toughness and Vickers hardness for the evaluation of $Y_2O_3$ surface machinability.