In this paper, an orthomodular lattice-valued pushdown automaton (e-VPDA) is introduced. This paper also provides the means of general subset-construction, and further proves the fact that an e-VPDA can accept the same l-valued language by final states and by another e-VPDA, with crisp transition relation and quantum final states at the same time. By using these relations, this paper is able to establish some algebraic level characterizations of orthomodular lattice-valued context-free languages and also focuses on the closed properties of these l-valued languages in details under standard operative conditions. Finally, this paper presents that an arbitrary orthomodular lattice-valued context-free grammar (e-VCFG) are mutually equivalently constructed with a e-VPDA, respectively.