A generalized Lie derivative operator suitable for use within the GHP formalism and the notion of preferred GHP tetrads relative to a vector are introduced. The usual homothetic or Killing equations are then replaced by an equivalent but much more manageable set of equations involving the commutators of this new operator with the four GHP derivative operators. This allows for an efficient treatment of the homothetic or Killing condition when constructing new solutions of Einstein's field equations or when obtaining the homothetic and/or Killing vectors for a given metric. Two applications are given. The first sheds new light on the vacuum twisting type N problem with one or two homothetic/Killing vectors. In the second we find the subclass of ail type N, and of all conformally flat, pure radiation metrics (with tau not equal 0) which possess one or more homothetic or Killing vectors.