Laurel didn't know Alex. She had seen her a few times around the network and at parties, but not intimately and not on the level of friendship. However, when Sara reached out to Laurel about speaking Alex about addiction and dealing with emotional pain while attempting to stay sober, Laurel could obviously not refuse. After all, she was no stranger to leaning on pain pills and alcohol to survive emotional trauma. Alex was clearly dealing with the same thing, having lost her husband, Pietro, a few weeks ago. Laurel knew how losing Sara had affected her; she'd almost given into the temptation of booze again in order to numb the pain caused by Sara's death. It was only through sheer willpower and a not so healthy lust for revenge that she didn't.
Obviously, Alex couldn't use such a concept as a crutch; you couldn't hurt the Dome despite how badly you might want to sometimes. All you could do was lean on the people who remained to help get through the pain of losing someone you loved and cared for. By reaching out to Sara, Alex was doing that and after her sister introduced them, the blond left, allowing Laurel and Alex to speak more privately among themselves. Laurel wanted Alex to know she could trust her. Nothing they said would leave this room and she was going to be there for her no matter what.
"It's no problem at all, Alex," Laurel replied quickly. She knew this had to be awkward for her. "I know the temptation of addiction...especially after you lose someone. It can be overwhelming."