Throughout Game of Thrones it's implied that Olenna Tyrell and Petyr Baelish were involved in Joffrey's murder and they pulled this off with the help of Sansa and Ser Dontos of House Hollard.
But could his grandfather and the Hand of the King be possibly involved with his murder?
Take a look at the fact that Joffrey acted weirdly three times with Tywin Lannister and that made him seriously angry.
As soon as he died he started giving life lessons to Tommen, and he was okay with killing children as he gave the order to kill infants of Rheagar and Elia Martell, and just before the Wedding Lady Olenna and Tywin had a little chat.