  We construct two-parameter families of integrable $\lambda$-deformations of
two-dimensional field theories. These interpolate between a CFT (a WZW/gauged
WZW model) and the non-Abelian T-dual of a principal chiral model on a
group/symmetric coset space. In examples based on the $SU(2)$ WZW model and the
$SU(2)/U(1)$ exact coset CFT, we show that these deformations are related to
bi-Yang-Baxter generalisations of $\eta$-deformations via Poisson-Lie T-duality
and analytic continuation. We illustrate the quantum behaviour of our models
under RG flow. As a byproduct we demonstrate that the bi-Yang-Baxter
$\sigma$-model for a general group is one-loop renormalisable.
