Tree-level S matrix for $\lambda$-deformed AdS3 strings

We consider the supersymmetric $\lambda$-deformation of ${\text{AdS}}_3\times {\text{S}}^3\times {\text{T}}^4$ superstrings and compute its perturbative bosonic tree-level worldsheet S matrix in the light-cone gauge. For generic values of $0\le \lambda <1$, we show that the worldsheet scattering remains compatible with integrability due to a non-trivial cancellation of non-elastic scattering processes. By contrast, the S matrix becomes ill-defined for $\lambda \to 1$, despite the fact that this limit reproduces the non-Abelian T-dual geometry up to an analytic continuation. This suggests that the $\lambda \to 1$ limit does not capture the full worldsheet dynamics of the T-dual theory.