I'm not sure Tyrion thinks she will send his army. Even the way he told Sansa, it sounded like he was trying to talk himself into believing it, even though he knows it is not going to happen. He averted his eyes from here when he told her the bit about Cersei having something to live for now. That is Tryion's only hope that Cersei might do the right thing as he knows how much she loves her family, but he is skeptical himself and possibly he may have even conspired with Cersei and outright knows what she plans but for love of family, Tyrion is hiding this.That leads me to my next point...one of the scenes that stuck out to me most was the one with Sansa and Tyrion. I loved that Sansa called Tyrion out on his bulls**t in believing that Cersei would ever send her army to aid the forces in the North. I can't believe Tyrion, of all people, took her at her word. The writing of his character has really started to suffer and his motivations and actions are beginning to not make any sense at all.
After watching the raid on the Lannister wagon train and the execution of the Tarly's you could see Tyrion has some serious reservation about the brutality of Dany
I think when it becomes clear Cersei is not coming (they will most likely find that out from Janmie) Tyrion will be in some serious hot water with Dany and will be seen as betraying Dany by keeping this from her