Lolita died shortly after her last meeting with Humbert (she was largely pregnant when she saw him and died in childbirth).  It took him awhile to find Quilty and shoot him.  Thus, no one, except Quilty and Humbert, knew about the relationship.  Humbert was tried and imprisoned for the murder of Quilty.  During his imprisonment, he wrote his confession.  I can't quite get the drift of this discussion.
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