OMG, how did I forget Two Gentlemen? Surely that rates as nearly on par with Lavinia and Lucrece's fates, especially as this happens in view of the audience?

Indeed! I think that, apart from Lavinia, Proteus's attempted rape of Silvia is the closest we get to this act in a Shakespearean play.

Also, another similarity between these is that, after the attempted rape, Silvia is then silent for the remainder of the play. In Lavinia's case, of course, the silence is enforced by her lack of a tongue. For Silvia, it seems more a case of poor writing by a young and inexperienced Shakespeare. Even so, the parallel is somewhat eerie.

I wonder if there's ever been a directorial choice to have Lavinia's rape happen onstage. I think it's unnecessary, as what comes immediately before and after is so horrible it would be overkill.

Ah, yes. Agreed completely!