Maybe it's because she was from the same clan or maybe, it's because they were from the same timeline.
Or maybe, it's because when they return to their timeline, she would be the only one to remember him.
For whatever reason, Azzy felt more comfortable with her than with either Claire or Gideon, although they were nothing more than strangers if one excludes their distant cousin relationship.
On top of that, as he was the reason she was stranded in this timeline, Azzy also felt guilty for her situation.
He decided to fulfill her demands as long as it doesn't cross his bottom line.
So, when she asked to talk after lunch, he agreed without hesitation. When she asked to eat lunch together with her, he complied.
And when she asked to sit with him, Azzy abandoned Gideon to sit with her but he didn't expect it would be comfortable despite eating in a crowd.