The author proves that if the isometric action of an arbitrary Lie group on a Lorentzian manifold is normalizable, then there is a unique infinitesimal principal type such that the orbits belonging to this type form an open and dense set. He also investigates the non-normalizable orbits and proves that in the Lorentzian case, such an orbit \(G(x)\) has light-like tangent spaces, and that for every point \(p \in G(x)\), there is a 1-parameter subgroup in \(G\) such that its orbit at \(p\) yields a light-like geodesic segment trough \(p\) contained in \(G(x)\).