The subject of this contribution is the study of the Lovász-Schrijver PSD-operator N + applied to the edge relaxation of the stable set poly-tope of a graph. We are particularly interested in the problem of characterizing graphs for which N + generates the stable set polytope in one step, called N +-perfect graphs. It is conjectured that the only N +-perfect graphs are those whose stable set polytope is described by inequalities with near-bipartite support. So far, this conjecture has been proved for near-perfect graphs, fs-perfect graphs, and webs. Here, we verify it for line graphs, by proving that in an N +-perfect line graph the only facet-defining subgraphs are cliques and odd holes.