Daenerys and Cersei will die
The Lannisters will attack and wreck Dany's caravan, but without Cersei's death, and when the two dies, Jaime, the King-Slayer, the man who killed Dany's father, and defeated the Mad King's daughter (he might be merciful and let her live to be raped by the soldiers or put in the dungeon there to stay forever), and the brother to Cersei, will become rightful king with King's Landing's support, both from the people and many of the lords.
The Lannisters will absorb Dany's caravan and kill many of the Unsullied and Dothraki. Jaime will pardon Tyrion and accept him into the family along with most of Dany's trusted when they bend the knee.
Jon Snow, who doesn't have any problem with either Tyrion nor Jaime, will ask to ally in order to defeat the white walkers. Then Jon Snow might become the Lord of the North and Winterfell and Jaime as King of the Seven Kingdoms. That's how it's going to be.
Until season 8 when Arya kills Jaime and Jon learns of his heritage and become the king of King's Landing.