High-power operation of conventional GaN-based light-emitting diodes (LEDs) is severely limited by current crowding, which increases the bias voltage of the LED, concentrates light emission close to the p-type contact edge, and aggravates the efficiency droop. Fabricating LEDs on thick n-GaN substrates alleviates current crowding but requires the use of expensive bulk GaN substrates and fairly large n-contacts, which take away a large part of the active region (AR). In this work, we demonstrate through comparative simulations how the recently introduced diffusion-driven charge transport (DDCT) concept can be used to realize lateral heterojunction (LHJ) structures, which eliminate most of the lateral current crowding. Specifically in this work, we analyze how using a single-side graded AR can both facilitate electron and hole diffusion in DDCT and increase the effective AR thickness. Our simulations show that the increased effective AR thickness allows a substantial reduction in the efficiency droop at large currents, and that unlike conventional 2D LEDs, the LHJ structure shows practically no added efficiency loss or differential resistance due to current crowding. Furthermore, as both electrons and holes enter the AR from the same side without any notable potential barriers in the LHJ structure, the LHJ structure shows an additional wall-plug efficiency gain over the conventional structures under comparison. This injection from the same side is expected to be even more interesting in multiple quantum well structures, where carriers typically need to surpass several potential barriers in conventional LEDs before recombining. In addition to simulations, we also demonstrate selective-area growth of a finger structure suitable for operation as an LHJ device with 2µm distance between n- and p-GaN regions.