Summary: Following [“Integrable 2d sigma models: quantum corrections to geometry from RG flow”, Nucl. Phys., B 949, Article ID 114798, 17 p. (2019; doi:10.1016/j.nuclphysb.2019.114798)], we continue our investigation of the relation between the renormalizability (with finitely many couplings) and integrability in 2d \(\sigma\)-models. We focus on the “\(\lambda\)-model,” an integrable model associated to a group or symmetric space and containing as special limits a (gauged) WZW model and an “interpolating model” for non-abelian duality. The parameters are the WZ level \(k\) and the coupling \(\lambda\), and the fields are \(g\), valued in a group \(G\), and a 2d vector \(A_{\pm}\) in the corresponding algebra. We formulate the \(\lambda\)-model as a \(\sigma\)-model on an extended \(G \times G \times G\) configuration space \((g, h, \overline{h})\), defining \(h\) and \(\overline{h}\) by \(A_+ = h \partial_+ h^{-1}\), \(A_- = \overline{h} \partial_- \overline{h}^{-1}\). Our central observation is that the model on this extended configuration space is renormalizable without any deformation, with only \(\lambda\) running. This is in contrast to the standard \(\sigma\)-model found by integrating out \(A_\pm\), whose 2-loop renormalizability is only obtained after the addition of specific finite local counterterms, resulting in a quantum deformation of the target space geometry. We compute the 2-loop \(\beta\)-function of the \(\lambda\)-model for general group and symmetric spaces, and illustrate our results on the examples of \(\mathrm{SU} (2)/ \mathrm{U}(1)\) and SU(2). Similar conclusions apply in the non-abelian dual limit implying that non-abelian duality commutes with the RG flow. We also find the 2-loop \(\beta\)-function of a “squashed” principal chiral model.