  We propose the approach for a lattice investigation of light-cone
distribution amplitudes (LCDA) of heavy-light mesons, such as the $B$-meson,
using the formalism of parton pseudo-distributions. A basic ingredient of the
approach is the study of short-distance behavior of the $B$-meson Ioffe-time
distribution amplitude (ITDA), which is a generalization of the $B$-meson LCDA
in coordinate space. We construct a reduced ITDA for the $B$-meson, and derive
the matching relation between the reduced ITDA and the LCDA. The reduced ITDA
is ultraviolet finite, which guarantees that the continuum limit exists on the
lattice.
