Marine hydrokinetic turbines are a promising source of renewable energy, but the costs of existing cross-flow turbine designs are too high. In order to develop new designs with reduced costs, there exists a need for a low-order computational model that is simultaneously fast, accurate, and robust. Herein, we present a novel theoretical model for the analysis of cross-flow propellers and turbines based on the vortex lattice method (VLM). In order to overcome the limitation that the VLM ignores viscous effects (such as trailing-edge flow separation), we present a novel method to account for viscous-thickness-load coupling (VTLC). In order to overcome the difficulty that wake passages cause the VLM to be unstable, we present the panel-averaged induced velocity for the influence of wake vortices on the blades. Herein, we describe our model and provide verification versus RANS CFD. Results show that our VLM + VTLC model predictions are three times more accurate than prior low-order models (i.e. three times lower root mean square error to high-fidelity RANS results) yet 10,000 times faster than RANS over a wide range of operating conditions.