The order here seems to be wrong, it should be who(live,woman), right?  Or is Ben asking for this reversed order?

In fact, I'm thinking that the correct thing to generate here is who(be, live) since the semantic function of "who" in this sentence is to disambiguate the woman -- we want to know  which woman it is, its the one who lives next door.  Since the head of the main sentence is "be" and the head of the dependent clause is "lives", the who relation should connect these two heads... right?

Ben, have you looked at this?