We employ two-dimensional (2-D) self-consistent physical modeling of a particularly promising lateral current injection laser reported recently in the literature to gain insight into the physical mechanisms governing the operation of this family of devices. We demonstrate the substantial benefits to be obtained from improved hole injection facilitated by relatively light p-type doping of barrier layers; from lateral shifting of the transverse junction to improve the overlap between the photon field and material gain; and from creating a lateral heterobarrier via quantum-well intermixing in order to confine carriers in the lateral direction. We find that with a number of relatively minor physically motivated modifications to existing fabrication processes, lateral injection lasers have the potential to exhibit greatly improved performance characteristics and to realize thereby their tremendous potential as enablers of optoelectronic integrated circuits and novel device structures.