The V-Nθ sector of the Lee model with Galilean invariance is studied by making use of the clothing transformation technique. We construct the most general unitary clothing transformation in the sector, by representing it in the basis of the bare states and find that a simple condition must be satisfied by the transformation functions in order to obtain a good potential description for the Nθ interaction. It turns out that if the Hamiltonian has at least one proper eigenstate such a transformation is always possible. Furthermore we show that in the limit of infinite coupling constant and infinite internal energy of the V-particle the potential goes to a well-defined form, which yields the limit of the scatteringT-matrix, while at the same time the «clothed» states become the bare ones. In particular the «bound-state limit» (Z → 0) is obtained in a natural way.