Control of order-disorder phase transitions is a fundamental materials science challenge, underpinning the development of energy storage technologies such as solid oxide fuel cells and batteries, ultra-high temperature ceramics, and durable nuclear waste forms. At present, the development of promising complex oxides for these applications is hindered by a poor understanding of how interfaces affect lattice disordering processes and defect transport. Here we explore the evolution of local disorder in ion-irradiated La$_2$Ti$_2$O$_7$ / SrTiO$_3$ thin film heterostructures using a combination of high-resolution scanning transmission electron microscopy (STEM), position-averaged convergent beam electron diffraction (PACBED), electron energy loss spectroscopy (STEM-EELS), and textit{ab initio} theory calculations. We observe highly non-uniform lattice disordering driven by asymmetric oxygen vacancy formation across the interface. Our calculations indicate that this asymmetry results from differences in the polyhedral connectivity and vacancy formation energies of the two interface components, suggesting ways to manipulate lattice disorder in functional oxide heterostructures.