We characterize Lie centralizer, Lie derivations and generalized Lie 2-derivations at zero products on triangular algebras without assuming unity. Further more, the Lie centralizers, Lie derivations and generalized Lie 2-derivations will be described for triangular algebras. Also, several examples are presented which illustrate limitations on extending some of the theory developed. The obtained results will be used for upper triangular matrix algebras (not necessarily unital) and nest algebras. Our results will also generalize some of the previous results.
