In Game of Thrones S04E02, "The Lion and the Rose", Joffrey Baratheon dies by drinking poisoned wine. The soldiers take Tyrion Lannister as prisoners and sentence him to death. Later he escapes.
In S07E03 it is revealed that it was Olenna Tyrell's plan with Littlefinger to poison Joffrey to avoid Margery Tyrell's wedding with Joffrey. Jaime Lannister says this to Cersei.
Even in the Game of Thrones finale, when Ser Brienne of Tarth updates the history of Jaime Lannister, it is written,
After the murder of King Joffrey I by Tyrion Lannister served under Tommen I
Do the common folk, Lords and ladies of Westeros or the seven kingdoms know who really poisoned Joffrey? Do they still think it was Tyrion Lannister?