  Motivated by the works of Wang [Y. Wang, \textit{Lie (Jordan) derivations of
arbitrary triangular algebras,} Aequationes Mathematicae, \textbf{93} (2019),
1221-1229] and Moafian et al. [F. Moafian and H. R. Ebrahimi Vishki,
\textit{Lie higher derivations on triangular algebras revisited,} Filomat,
\textbf{30}(12) (2016), 3187-3194.], we shall study Lie higher derivations of
arbitrary triangular algebras. In fact, it is shown that every Lie higher
derivation on an arbitrary triangular algebra is proper, using the notion of
maximal left (right) ring of quotients.
