  In this note, we study the action of $O(d,d)$ transformations on the
integrable structure of two-dimensional non-linear sigma models via the doubled
formalism. We construct the Lax pairs associated with the $O(d,d)$-transformed
model and find that they are in general non-local because they depend on the
winding modes. We conclude that every $O(d,d;\mathbb{R})$ deformation preserves
integrability. As an application we compute the Lax pairs for continuous
families of deformations, such as $J\bar{J}$ marginal deformations and TsT
transformations of the three-sphere with $H$-flux.
