  This article is a continuation of the work "Tropical Lagrangian
multi-sections and smoothing of locally free sheaves over degenerated
Calabi-Yau surfaces". We generalize the notion of tropical Lagrangian
multi-sections to any dimensions. Together with some linear algebra data, we
construct a special class of locally free sheaves, called tropical locally free
sheaves. We will also provide the reverse construction and show that there is a
1-1 correspondence between isomorphism classes of tropical locally free sheaves
and tropical Lagrangian multi-sections modulo certain equivalence.
