The present investigation aims to investigate the machinability performances of graphene solid lubricant (S) deposited on dimple texture (T1-S), novel honeycomb texture (T2-S), and novel broken-parallel textures (T3-S) during dry turning of Inconel 713C has been carried out and compared with dry (D) textured tools (T1-D, T2-D, and T2-D). L24 orthogonal design was used to design the experiments by considering conditions (dry and solid lubricant), textured type, cutting speed, and feed rate. The experimental results reveal that the honeycomb without and with graphene (T2-D and T2-S) effectively reduced the generated cutting temperature by 14.5 % and 22.4 %, cutting force by 34.6 % and 39.4 %, surface roughness by 14.3 % and 22.4 % and tool flank wear by 11.9 % and 2.3 % compared dimple and broken parallel textured inserts. The honeycomb tool (T2-D and T2-S) exhibited shear angle increased by 7.45 % and 6.5 % and 29.3 %, and 33.33 % than dimple under dry and graphene textured cutting tool. The chip reduction coefficient was <1.5, resulting in an increased shear angle and decreased friction coefficient in graphene-deposited honeycomb texture conditions. The major mechanism credited to the improved performance of honeycomb with graphene tool was reduced chip curl diameter and chip width by 3.3 % and 5.7 % compared to other tools. SEM images showed that all textured inserts' primary tool wear mechanisms on the tool surface were built-up edges, micro-chipping, adhesions, and abrasions. EDS analysis and following elemental plotting showed the strong presence of workpiece constituents on the flank surface. But, the influence of adhesion and abrasion was more noticeable for all dry-textured tools. The findings of this study indicate that honeycomb textured tools are a superior alternative to dry machining of Inconel 713C. Additionally, broken-parallel textured tools were more effective than textured dimple tools.