Transport and emplacement of pahoehoe lava is often dominated by random influences, such as budding, small-scale variations in topography, degree of inflation, and variations in how the skin cools, stretches, and cracks. A random walk model is used to describe the transport of small pahoehoe lobes when random effects are a significant influence on emplacement. We derive the stochastic formalism for random movements on a two-dimensional grid. Our formulation features correlation and bias that determine the degree of randomness in the random walk of each parcel of lava. Qualitative and quantitative predictions of the random walk are compared with observations and data for pahoehoe lobes in Hawaii. The correlated random walk quantitatively describes lobe thickness transects, whereas the uncorrelated random walk only reproduces the meandering of small filaments of a few toes. Correlation expresses momentum effects and a chain of memory from the flow front to the source of lava supply. The correlated random walk features a channel-forming regime that decays with distance from the source of lava supply. The theory can also be interpreted in the context of a time-dependent planar flow. When many parcels of lava participate, the overall shape of a one-dimensional lobe has the appearance of a continuum wave. The types of processes contained in this basic random walk model explain the multitude of concurrent or overriding features found in broad fields of toes. The formalism can thus be extended to simulate large fields of emplaced pahoehoe in either terrestrial or planetary settings.