Possibly, but how do you imagine Tywin would deal with Cersei, Jamie or much less Tyrion lieing to his face several times? Cersei says that Tywin NEVER smiles at his funeral, but he seems to be pretty friendly and willing to discuss his past including the potential family "weakness" of Jamie's dyslexia. He had Tyrion's wife gang raped and forced him to particpate. He forced Jamie to lie and say Tysha was a whore he paid. He gave up on Jamie when he was in captivity at Riverrun, which is why he sent Tyrion to be the Hand in the first place, because he was the last son he had. And finally disowned Jamie when he insisted on retaining his position as head of the Kingsguard.
Tywin had the deserters at the Battle of Blackwater's knees broken with hammers to serve as a visual warning to any further desertion, and had his men rape, murder and burn the villages of the Riverlands to provoke the Starks to attack him at Harrenhal. Tywin did not suffer disloyalty in his vassals and was not a very sympathetic person, but apparently in his cupbearers his patience is much higher.
He did all of those things, and yet is still a complex, driven human, and not a complete monster like Gregor or Ramsay. He's only brutal when he finds it necessary, and it's absurd to think he'd find it necessary to discipline a foraged cupbearer over a minor, understandable, and ultamitely inconsequential lie, particularly when that cupbearer is, in her own way, showing more competence than some of his battlefield commanders. The book gives us backstory and internal monologue, while the series invents a scene with Arya, but both are to the same effect. If you choose to believe that Tywin is a Complete Monster and that the show ruins this for you, that's your prerogative, but there are plenty of people that are very knowledgeable of the books that would strongly disagree with you.
At any rate it still comes back to the fact that the only similarities are that Arya and Tywin are at Harrenhal and Jaqen has offered her 3 deaths, and Gendry is serving as a blacksmith. So I still stand by the statement that there are more changes than similarities in the story line, and so trying to predict what will happen next based on the books is not particulary likely to give you a good prediction.
This is, quite simply, not true. The similarities are plentiful, but you have to dig a level deeper than the superficialities you're looking at. Like I said, the first of Arya's names is wasted on an inconsequential (but despicable) soldier, driven in part or in whole by the fact that Arya didn't really trust Jaqen and thought it might be a trap. It doesn't matter that the name was The Tickler instead of Chiswyck (other than the fact that it deprives Arya of a moment in Book 3, but really that moment was lost - altered, really - when the show didn't have the time to focus quite so much on the torture).
The second death was done out of an immediate personal need, in both the show and the book. The name and context were different (and the show certainly amped up the immediate tension - again, a consequence of book-to-screen adaptation) but thematically, they were identical.
So it's perfectly reasonable to presume that the third death will follow the theme of the books, which was Arya making a choice that she felt would best help her brother's war effort, and realizing that she could manipulate Jaqen into going above and beyond the strict three-death limit by naming Jaqen himself. The fact that she was willing to snatch a message from Tywin's table to further the Stark war effort foreshadows that that's already on her mind, and frankly, it's such an awesome Arya moment that D&D would be loathe to lose it. Though they've changed the details, they have
built toward it.
That it's going to be different in the details is a foregone conclusion. We might as well complain that it's telling the story using pictures and sounds instead of just words. But just because it shifts details here and there doesn't mean that they're changing things Just Because, and doesn't mean they're not building to the Big Moments that are straight from the books. It's not impossible to predict, you just need to use different tools.