I will try to explain what I believe they are attempting to display during this episode.
1. The point to having Euron pretend to abandon Cersei is to set up the Targaryen alliance in a way the surprise can defeat overwhelmingly superior forces. Right now Cersei is outnumbered at least 5 to one. She has no *nukes AKA dragons, she has only a superior Navy. She owns the seas through Euron. With Euron displaying erratic behavior to start the meeting, it was a public display of discord and a lack of discipline amongst her force commanders, specifically, with her only critical capability. The erratic behavior is a very public display of weakness in the face of their enemies. I believe this will ultimately fail though. Something tells me Dario Naharis might be in play here.
2. The only real way they could have planned this is if they have an insider in Jon or Dany's forces. I have no idea who it is, but I'd say Varys if anyone. For all we know it could have been Littlefinger. Great thing Arya has the ability to snatch his face off and get close to one of the last people on her little list (Cersei).
3. It was necessary, but everyone in the world knew that she would lie. Sadly, Tyrion fell for her lies. I believe he actually just wanted some closure in the loss of his niece and nephew. I would LOVE to know what his and Cersei's conversation was about after the scene cut.
4. Sansa and Arya fooling LF was absolutely necessary. It's the most cathartic justice the series could have possibly served. In the north, you must pass the sentence and swing the sword. I don't know how they are about Ladies in that whole procedure, but I think they nailed this. LF was taken out by the use of his greatest strength. His voice. He was undone by it over the past 3 episodes. Oh, by the way, Bran (a stark, and the heir to Winterfell if he'd wanted it) was able to supply every bit of evidence needed. D&D just didn't have time to show how this happened. Remember the old 3ER was able to take folks back with him to points in history...Now, the viewer just has to believe that he has done that with those necessary (Yon Royce, Sansa, Arya, Lord Glover, Lyanna Mormont and any other vessel lords, or banner men to Winterfell). There was a scene that was cut showing Sansa asking Bran to help in this case.
5. Tyrion is not upset as a lover. He is upset as he believes the purpose of his life (As he stated in Season 5 multiple times) is to guide Dany to the Iron throne. With Jon / Aegon as her King / Boyfriend / paramour / whatever they plan to call it, Jon's advice would carry more weight than Tyrion's, even as her hand. He is also the uber intelligent person that understands that Dany is more than likely going to make some sort of hyper emotional idiotic sacrifice at a critical moment in battle to save Jon.
Edited immediately as I forgot one of my points in part of #1.