  We prove the existence of a separable approximately ultra-homogeneous Banach
lattice $\mathfrak{BL}$ that is isometrically universal for separable Banach
lattices. This is done by showing that the class of Banach lattices has the
Amalgamation Property, and thus finitely generated Banach lattices form a
metric Fra\"iss\'e class. Some additional results about the structural
properties of $\mathfrak{ BL}$ are also proven.
