Recent computational studies have simulated a mode of distributed premixed combustion where turbulent mixing plays a significant role in the transport of mass and heat near the reaction zone. Under these conditions, molecular transport processes play a correspondingly smaller role. A consequence of burning in this regime is that a change in the gas mixture composition can occur within the flame zone, which modifies the burning rate. The composition depends on the Lewis number (ratio of molecular heat to mass diffusivity), and so the response to the transition to distributed burning will be different for fuels with different Lewis numbers. In this paper, we examine the role of Lewis number on flames in the distributed burning regime. We use high-resolution three-dimensional flame simulations with detailed transport models to explore the turbulent combustion of a range of fuels, specifically lean premixed hydrogen, methane and propane mixtures. The response of the burning rate is found to be more pronounced in hydrogen than in the other fuels.