Light Field Networks, the re-formulations of radiance fields to oriented rays, are magnitudes faster than their coordinate network counterparts, and provide higher fidelity with respect to representing 3D structures from 2D observations. They would be well suited for generic scene representation and manipulation, but suffer from one problem: they are limited to holistic and static scenes. In this paper, we propose the Dynamic Light Field Network (DyLiN) method that can handle non-rigid deformations, including topological changes. We learn a deformation field from input rays to canonical rays, and lift them into a higher dimensional space to handle discontinuities. We further introduce CoDyLiN, which augments DyLiN with controllable attribute inputs. We train both models via knowledge distillation from pretrained dynamic radiance fields. We evaluated DyLiN using both synthetic and real world datasets that include various non-rigid deformations. DyLiN qualitatively outperformed and quantitatively matched state-of-the-art methods in terms of visual fidelity, while being 25 - 71× computationally faster. We also tested CoDyLiN on attribute annotated data and it surpassed its teacher model. Project page: https://dylin2023.github.io.