A recent numerical study of turbulence-flame interactions in lean premixed hydrogen, where the Lewis number was approximately 0.36, observed that flames at different equivalence ratios presented significantly different behavior despite having the same Karlovitz and Damkohler numbers. This differing behavior is due to the thermodiffusively-unstable nature of low Lewis number flames. In more than one dimension, differential diffusion focuses fuel into hot regions increasing the local burning rate, which was found to affect the leaner hydrogen flames more significantly. Ultimately, this difference between idealized flat flames and freely-propagating flames undermines the characterization of turbulent flames through Karlovitz and Damk¨ohler numbers based on flat laminar quantities. This paper considers refining the definitions of these dimensionless numbers by replacing the flat laminar flame values with freely-propagating values. In particular, we perform three-dimensional simulations of freely-propagating flames over a range of equivalence ratios, and use data from those simulations to define modified Karlovitz and Damk¨olher numbers. We then perform a series of turbulent flame simulations that show that defining Karlovitz and Damk¨olher numbers based on the freely-propagating flames effectively eliminates dependence on equivalence ratio.