Dually residuated lattice ordered monoids (DRl-monoids) are common generalizations of, e.g., lattice ordered groups, Brouwerian algebras and algebras of logics behind fuzzy reasonings (MV -algebras, BL-algebras) and their non-commutative variants (GMV - algebras, pseudo BL-algebras). In the paper, lex-extensions and lex-ideals of DRl-monoids (which need not be commutative or bounded) satisfying a certain natural condition are studied.