He had committed that murder because Quilty had lured the young Dolores Haze away from him.  
He periodically plays chess with Gaston Godin and obtains sleeping pills from Dr. Byron, using them to keep his second wife under control.  His first wife Valeria left him for a cabdriver, with whom he has an unproductive discussion of Jean Christophe.  All of this is related in his manuscript, which is edited by C.C. Clark and John Ray Jr and which was written during his time in prison for the murder of Clare Quilty.  He had committed that murder because Quilty had lured the young Dolores Haze away from him.  FTP, name this man who had an affair with the titular nymphet in Vladimir Nabokov's Lolita.
He periodically plays chess with Gaston Godin and obtains sleeping pills from Dr. Byron, using them to keep his second wife under control.  
Humbert Humbert