Our earlier studies showed that the key Brooks-Corey (B-C) hydraulic parameters ( Ksat, air-entry pressure head, and dependant parameters) were also strongly related to the pore-size distribution index (lambda), and the lamda could scale B-C formulation of the soil-water retention curves below the air-entry pressure head, as well as infiltration, across widely dissimilar (Sandy to clayey) eleven soil textural-mean soils. In this work, we first showed that there were strong empirical functional relationships of the parameters of the empirical Lewis (Kostiakov) infiltration equation with lamda, as well as with Ksat, for Instantaeously-ponded water infiltration, for which this equation has been used in the past. The Lewis (Kostiakov) parameters vs. lamda or Ksat (Ksat was better) provided more compact and explicit relationships across diverse soil classes. We then extended the Lewis equation to non-instantaneous ponding (e.g., rainfall) infiltration conditions, and showed fairly strong relationships of the new parameters with lamda and Ksat there as well across the textural classes for four different rain intensities. These relationships could be used to scale and estimate infiltration across these classes. We also investigated how these relations could be used in the field for layered soils and non-constant rain intensities. This study is a breakthrough in our understanding of the soil water relationships and scaling among soil textural classes, that could serve as a basis for describing spatial variability of soil water on the landscape for site-specific management and for scaling up results in modeling from plots to fields to watersheds.