We consider charge carriers that undergo nearest-neighbor hopping among the sites of a binary random lattice, each site of which is associated with one of two possible energies E1 or E2. A general and recently observed feature of this problem not predicted by previous treatments of disordered hopping models is a crossover between trap-limited conduction and percolation. We introduce new energy-projected equations of motion whose solutions reveal the deep conductivity minimum associated with this phenomenon, and compare the results predicted to numerical simulations.