Pressure vessels and their components are commonly designed with the ASME Boiler and Pressure Vessel Codes. One of the requirements when pursuing the design by analysis route is to design these equipment against ductile local failure criterion provided in the codes. However, the ductile local failure criterion in the ASME codes only accounts for the stress triaxiality (T) as a stress state measure. Recent work has shown that ductile failure highly depends on the stress state characterized by both T and the Lode parameter L, which is related to the third deviatoric stress invariant. In this study, the effect of stress state characterized by both T and L is investigated for six different steel grades with different material strength levels. To establish the ductile failure loci for the six steel grades with respect to T and L, experiments were conducted on two different specimen geometries. The L parameter is controlled by the specimen configuration, where the round notched bar specimen corresponds to axisymmetric tensile conditions (L = −1) and the flat notched specimen corresponds to plane strain loading conditions (L = 0), whereas T is controlled by introducing a notch at the center of the specimens. A Lode sensitivity parameter (LS) is defined based on the experimental results and revealed that the steel grades with ultimate strength higher than a certain threshold value (450 MPa) exhibit sensitivity to the Lode parameter. The Lode sensitivity was quantified, and the results showed that the LS increases with increase in the ultimate strength of the steel grade. The results were incorporated to enhance the original ASME local failure criterion by accounting for T, L, and LS to accurately assess ductile failure in high-strength steels. The application of the enhanced failure locus in a design analysis of a pressure vessel made of a high-strength steel grade is demonstrated, which showed that the original ASME criterion, as compared to the enhanced criterion in this study, is not capable of predicting ductile failure and hence rendering a rather nonconservative design. It is concluded that the enhanced local failure criterion is recommended to be used for the design of pressure vessels and their components made of steel grades with an ultimate strength higher than the threshold value.