Lena's family could not be described as close. It's not that they're naturally chilly folks, either; it's that the cure for deliria makes them that way. The cure makes people seem stoic and uncaring, and it puts up walls between family members.
Even though Lena's Aunt Carol and Uncle William took her in after her mom and dad died, they don't exactly dote on her. Lena often longs for a hug, a comforting pat, any sign of affection from her family, but she never gets it. She doesn't get affection from her sister, Rachel, either, and Lena really holds this against her.
However, Lena's aunt Carol does care for her, in her own way. She may be strict, and a bit distant, but she spends a lot of time helping Lena prepare for her evaluation. While the evaluation might not be inherently a good thing, it's not like Aunt Carol—or Lena for that matter—are the type of people to rally against it.
By helping Lena prepare, she's doing what she can to ensure a good life for her niece… as good a life as one can have in this controlling dystopia. And heck, Aunt Carol is a lot nicer to Lena than she is to her own daughter, Grace. Grace is mute, and Carol calls her "as dumb as a rock" (2.7).
Lena doesn't think Grace is that dumb, though. Mainly because she's heard Grace speak before, but also because Grace is the one who saves Lena in the end. She screams, distracting the family members who are trying to restrain Lena and keep her from fleeing into Alex's arms.
This cements Grace as a "good" family member in Lena's selfish mind. To Lena, people are only good if they do something to help her be with Alex, her one true love.