Are any finitely generated reflexive module a second syzygy?
(I´m thinking especially in normal noetherian domains)
Are any divisorial lattice a second syzygy? (I´m thinking especially in Krull domains)
Over a normal domain (in fact, you only need Gorenstein in codimension 1, being second syzygy and reflexive are equivalent). This is Theorem 3.6 of Evans-Griffith "Syzygies" book.