Turning operation of Ti6Al-4V alloy using conventional lathe is challenging owing to high hardness, high strength to weight ratio of the work material. Past researcher works have claimed that as compared to dry machining, cutting using minimum quantity lubrication (MQL) technique can enhance the quality of machining output measures. But, at the same time, the use of different cutting fluids is found hazardous, non-eco-friendly, vulnerable to human health and surrounding. To overcome this problem, the present research work investigates the effect of using soybean oil in MQL for turning of Ti6Al-4V alloy. A comparative study on the performance of turning operation under dry and MQL environments has been carried out. The effects of the machining parameters such as speed, feed and depth of cut on machining quality measures such as material removal rate (MRR), tool wear rate (TWR) and surface roughness (SR) are also investigated. Also, to further enhance the quality of machining performance measures, gray correlation-based technique for order of preference by similarity to ideal solution (GC-TOPSIS) approach combined with fuzzy weights is employed to identify the optimal parametric combination. It has been found that to attain the best machining outputs, the optimal parametric combination should be set as speed = 575 rpm, feed rate = 0.02 mm/rev, and depth of cut = 0.1 mm. On the other hand, turning of Ti6Al-4V alloy under MQL cutting environment has shown significant improvement of 11, 18.18, and 46.39% for MRR, TWR, and SR, respectively, as compared to dry cutting. Analysis of variance results identifies spindle speed as the most influential processes parameter for both the dry and MQL cutting environments in determining the quality of measured response values. The developed surface plots will help a process engineer in selecting the most appropriate combination of process parameter for attaining desired performance measures.