  Recently the authors D. Bravo, M. Lanzilotta, O. Mendoza and J. Vivero gave a
generalization of the concept of Igusa-Todorov algebra and proved that those
algebras, named Lat-Igusa-Todorov (LIT for short), satisfy the finitistic
dimension conjecture. In this paper we explore the scope of that generalization
and give conditions for a triangular matrix algebra to be LIT in terms of the
algebras and the bimodule used in its definition. As an application we obtain
that the tensor product of an LIT $\mathbb{K}$-algebra with a path algebra of a
quiver whose underlying graph is a tree, is LIT.
