A recently developed nondestructive method was used to investigate the stress build-up in chemically strengthened lithium aluminosilicate glass. We utilized an updated version of the gradient scattered light method, which now enables more precise determination of the depth coordinates, recovering a more detailed stress profile around the knee. The main motivation of the work was to characterize and optimize the development of the knee-shaped breaking point in stress profile in lithium aluminosilicate glass prepared by the Saunders-Kubichan method of one-step strengthening in a mixture of KNO3+NaNO3 molten salt bath. In the industry, a two-step process is still commonly used to build such a stress profile; the one-step strengthening will simplify the process as well as save the cost. Compared to previous studies, which used a destructive method based on transmitted light photoelasticity, we found that in the samples ion exchanged for 24 hours, the knee-shaped breaking points were situated two times deeper whereas the case depths were 28% shallower. The measured stress profiles were validated by stress equilibrium and by comparison to Na+ ion concentration profiles.