A numerical code for solving various Lyα radiative transfer (RT) problems is presented. The code is suitable for an arbitrary, three-dimensional distribution of Lyα emissivity, gas temperature, density, and velocity field. Capable of handling Lyα RT in an adaptively refined grid-based structure, it enables detailed investigation of the effects of clumpiness of the interstellar (or intergalactic) medium. The code is tested against various geometrically and physically idealized configurations for which analytical solutions exist, and subsequently applied to three different simulated high-resolution "Lyman-break galaxies," extracted from high-resolution cosmological simulations at redshift z = 3.6. Proper treatment of the Lyα scattering reveals a diversity of surface brightness (SB) and line profiles. Specifically, for a given galaxy the maximum observed SB can vary by an order of magnitude, and the total flux by a factor of 3-6, depending on the viewing angle. This may provide an explanation for differences in observed properties of high-redshift galaxies, and in particular a possible physical link between Lyman-break galaxies and regular Lyα emitters.