  We continue our study of $\lambda$-deformed $\sigma$-models by setting up a
$1/k$ perturbative expansion around the free field point for cosets, in
particular for the $\lambda$-deformed $SU(2)/U(1)$ coset CFT. We construct an
interacting field theory in which all deformation effects are manifestly
encoded in the interaction vertices. Using this we reproduce the known
$\beta$-function and the anomalous dimension of the composite operator
perturbing away from the conformal point. We introduce the $\lambda$-dressed
parafermions which have an essential Wilson-like phase in their expressions.
Subsequently, we compute their anomalous dimension, as well as their four-point
functions, as exact functions of the deformation and to leading order in the
$k$ expansion. Correlation functions with an odd number of these parafermions
vanish as in the conformal case.
