This article presents the friction test results for cold-rolled low-carbon DC06 steel sheets, which are commonly processed into finished products using sheet metal forming methods. A strip drawing test with flat dies was used in the experimental tests. The strip-drawing test is used to model the friction phenomena in the flange area of the drawpiece. The tests were carried out using a tester that enabled lubrication with a pressurised lubricant. The friction tests were carried out at different nominal pressures, oil pressures, and friction conditions (dry friction and oil lubrication). Oils destined for deep-drawing operations were used as lubricants. Neural networks with radial base functions (RBFs) were used to explore the influence of individual friction parameters on the value of the coefficient of friction (COF). Under lubrication with both oils considered, the value of the COF increased with decreasing oil pressure. This confirms the correctness of the concept of the device for reducing friction in the flange area of the drawpiece. The developed concept of pressurised lubrication is most effective at relatively small nominal pressures of 2–4 MPa. This range of nominal pressures corresponds to the actual nip pressures when forming deep-drawing steel sheets. Under conditions of dry friction, the values obtained for the COF rise above 0.3, while under lubrication conditions, even without pressure-assisted lubrication, the COF does not exceed 0.2. As the nominal pressure increases, the effectiveness of the lubrication exponentially decreases. It was found that the Sq parameter carries the most information regarding the value of the COF. The RBF neural network with nine neurons in the hidden layer (RBF-8-9-1) and containing the Sq parameter as the input was characterised by an R2 of 0.989 and an error of 0.000292 for the testing set.