The effects of Lewis number (Le) on scalar dissipation rate transport of the reaction progress variable have been studied using 3-dimensional DNS data of freely propagating turbulent premixed flames with global Lewis number ranging from 0.34 to 1.2. It has been found that the effects of dilatation rate become increasingly strong with decreasing Le, and is particularly strong for the Le << 1 flames because of greater rate of heat release. Moreover, increasingly strong flame normal acceleration in flames with decreasing Le gives rise to countergradient transport for the turbulent flux of the scalar dissipation rate, whereas this flux exhibits gradient transport for flames with Le epsilon 1. This turbulent flux is observed to correlate with the behavior of the turbulent scalar flux and this behavior is used to propose an algebraic closure for the turbulent flux of the scalar dissipation rate. The modeling of nonunity Le effects on the unclosed terms arising from the density change across the flame front, the turbulence-scalar interaction, the correlation between scalar gradient and the gradient of reaction rate and the molecular dissipation have been addressed. The extent of reaction progress variable gradient alignment with the most extensive (compressive) principal strain rate is found to increase (decrease) with decreasing Le. This alignment behavior gives rise to a sink contribution arising from the turbulence-scalar interaction in the Le << 1 flames. By contrast, the turbulence-scalar interaction acts predominantly as a source term, although this contribution becomes a sink toward the burned gas side for the Le epsilon 1 flames. It has been demonstrated that existing models for the unclosed terms originating from the density change across the flame front and the turbulence-scalar interaction cannot account for strengthening (weakening) of heat release effects when Le1 (Le1). Suitable modifications to these models have been proposed to account for nonunity Lewis number effects, and validated using direct numerical simulation data. A simple algebraic expression is suggested that successfully relates the scalar dissipation rate of normalized temperature to the scalar dissipation rate of the reaction progress variable in nonunity Lewis number turbulent flames.