One of the main problems during sheet metal forming is the reduction in coefficient of friction and separation of contact surfaces in order to eliminate buildups of the formed material on the forming tools. For this purpose, technological lubricants based on mineral or synthetic oils are usually used. Unfortunately, their removal from the drawn parts and their subsequent utilization pose many problems and are expensive. Environmentally benign lubricants based on vegetable oils with the addition of boric acid could be an effective alternative to lubricants based on mineral and synthetic oils; however, the solubility of boric acid in oils is limited. Therefore, the paper proposes new, effective, and environmentally friendly methods for applying boric acid to the metal sheet by spraying it on a thin rapeseed oil layer previously applied to the metal sheet or by spraying a 25% solution of boric acid in methyl alcohol onto the sheet. The effectiveness of such lubrication was assessed on the basis of the so-called strip drawing test, Erichsen cupping test, and formation of cylindrical drawn parts in industrial conditions. The tests showed that the addition of boric acid was most effective for forming the DC01 steel sheet, reducing the coefficient of friction by about 60% compared to base oil lubrication. Although its usefulness is lower in the case of other frictional pairs, it eliminates the phenomenon of the formed material sticking to the tool, thus extending the life of the forming tools. The use of the proposed solution reduces production costs and indirectly boosts environmental protection. Moreover, an explanation of the tribological mechanism contributing to the lubrication action of boric acid is given.