Aryeh Lev is Asher's dad: a scholar, world traveler, and hardcore traditionalist. He's the Rabbi's right-hand man, dispatched all over the world to build yeshivas and spread Jewish teachings. He is also directly responsible for helping smuggle Jewish people out of Russia, where Stalin is organizing anti-Semitic killings. He is disappointed that his son isn't a scholar (and lifesaving human trafficker) like himself, and grows increasingly distant from Asher throughout the book.
When it comes to fatherhood, Aryeh Knows Best. He is strong-willed, highly opinionated, and used to getting his way. Because he is a scholar who comes from a long line of scholars, he expects his son to take after him. When Asher doesn't, this doesn't exactly please Aryeh:
He said to me once, gazing at one of my drawings, 'You have nothing better to do with your time, Asher? Your grandfather would not have liked you to waste so much time with foolishness.' (12.5)
Aryeh is none too pleased and unafraid to show it. This makes it pretty unpleasant to be the person making Aryeh unhappy, and Asher is that person throughout this book. It is Aryeh's difficult relationship with Asher that forces Asher to exile himself from his family, eventually exchanging only a handful words with his father daily before he's banished from the family's house.
Aryeh is for the most part a devoted and loving husband to his wife Rivkeh, but he's not always the most understanding:
'Rivkeh, you're a mother. There's a child to raise..'
'I'm also a sister and a wife,' she said. They looked at each other in silence. (47.10-11)
Aryeh's failure to understand his wife's desires leads to significant fragmentation within the family. Although he does allow Rivkeh to continue pursuing her studies, he fails to think of her feelings while he's traveling, expecting her to parent Asher while he's off doing dangerous work for the Rabbi. Not exactly a supportive husband.
It's in his role as a scholar that Aryeh really shines: he loves reading the Torah, traveling for the Rabbi to rescue other Jews from murderous dictators like Stalin, long walks on the beach, and building Hasidic yeshivas all over Europe. His life's work is to carry on the tradition of hyper-religious scholarship established by his father and his father before him:
'Why do you study [the Torah] so often, Papa?'
He smiled and his eyes grew dreamy. 'My father liked to study it often, Asher.' (12.2-3)
Aryeh's devotion to his scholarship ends up being the thing that comes between him and his son. When faced with the choice between being a good and understanding father and being an observant and scholarly Jew, Aryeh ends up choosing the latter, devastating Asher and tearing apart his family.