The paper is part of a series of the author’s studies of intuitionistic linear propositional logic. Here, he succeeds to define syntactic correspondence between Lambek’s syntactic calculus LSC and a fragment of a sequent calculus for non-commutative intuitionistic linear propositional logic [the author, “Sequent calculus for intuitionistic linear propositional logic”, in: Proceedings of Heyting ’88, Chaika near Varna, Bulgaria, September 12-23, 1988, Plenum Press, London (to appear)]. The rest of the paper is devoted to problems of the semantics of these calculi.