The show never addresses a possible non-consensual union between Aerys II and Joanna, but there definitely are moments like the one previously mentioned that could make a viewer wonder about Tyrion’s real lineage. At another point, Tyrion tells his father that, in the wake of the battle of Blackwater Bay — where Tyrion successfully defended King’s Landing and ended up with a huge facial scar as a result — he believes he deserves control of the Lannister fort Casterly Rock. How does Tywin respond? He lays into Tyrion: “You are an ill-made, spiteful little creature, full of envy, lust, and low cunning. Men’s laws give you the right to bear my name and display my colors, since I cannot prove that you are not mine. And to teach me humility the gods have condemned me to watch you waddle about wearing that proud lion that was my father’s sigil and his father’s before him.”
That feels fairly telling, especially when you pair it with the moment when Tyrion comes face to face with two massive dragons and lives to tell the tale. After Daenerys Targaryen (Emilia Clarke) locks up two of her dragons thanks to their destructive tendencies, Tyrion lets Viserion and Rhaegal loose from their chains, and the dragons don’t immediately barbecue him. The only other person on the show — besides Daenerys — to pull off this feat is Jon Snow (Kit Harington), who is, in fact, a secret Targaryen.