The B-meson physics plays a remarkable role in particle physics, both in a detailed examination of the Standard Model and in the search of new physics beyond the Standard Model. One of the most important functions describing the structure of the B-meson is its light cone distribution amplitude (LCDA). In this talk, I will discuss the the approaches for lattice investigation of LCDAs of heavy-light mesons, such as B-meson, using the formalism of quasi- and pseudo-distributions. The results reported in the talk might provide a basis for a practical computation of B-meson LCDA with lattice methods.