"absent-mindedly as her thoughts kept drifting to the boy"
I wouldn't use both, if her thoughts go back to Berin she is not focused on her task, so that was a bit of an overkill.
"(Berin, it’s Berin, she kept telling herself) and last night."
I think parentheses don't fit, I would just make the thoughts italic to indicate that those are the thoughts of the person. "kept drifting to the boy, Berin, it’s Berin, and last night."
"She paused – yes, I do."
What was she doing/saying what could be paused? I found that you could let her say something when she hands him his sweater. But no, she does nothing in that moment that could be paused.
"“T-t-t—thank you,” Lucy stuttered."
Hmm, I don't like that kind of indicating that she stutters. I would rather use "Thank... thank you." as she isn't disabled or has difficulties to pronounce "t".
"“I had to see something,” he said as he shrugged; back to Lucy."
As there is no one else on the roof the "back to Lucy" isn't really needed.
Those points struck me on the first read but the rest was pretty decent.
The only things that I can't explain or where I lack knowledge are how she fell off the roof, how he saved her and how it fits into the drug dealer picture and the importance of Gertrude as she appears in the beginning a few times.
"Lucy’s mother was out with Gertrude[...]" - Here it's fine, they are shopping, she is at home.
"[...]in her own apartment and Gertrude’s." - Why not simply "their apartments"?
"Her stomach slowed her, along with her sore body, after a hearty dinner of meatloaf with her parents and Gertrude." - I think it is too much. "[...]after a hearty dinner." is enough in this situation.
"Gertrude always spiced up conversation," - Additional information about Gertrude which is fine.