The first time they recognized each other as a family member was probably when Allen came back from his first mission.

Not long after Allen's enrollment to the Black Order, he was sent to a mission to obtain an Innocence, together with Kanda. I believe it was his first mission since he entered the Order. Both Allen and Kanda had already started to dislike each other, and they had opposite characters and opinions so it was quite a hard mission. After they accomplished the mission, Kanda was sent to another mission, while Allen was ordered to go back to the headquarters to deliver the Innocence to Hevlaska.

At the same time, there was a huge chaos developing in the headquarters. It all began with Komui's coming to the science department, showing off his latest invention to everyone: an omnipotent robot named Komurin II, which was like a duplicate of Komui's brain and personality. Therefore, they were hoping that Komurin can make their work easier.

Unfortunately, Komurin even had Komui's coffee-craving attitude copied in its brain. Therefore, it took a cup of coffee which Lenalee brought, and drank it. Startled, Lenalee asked his brother, "Can Komurin drink coffee?" Komui thought that it was a silly question, because "Even though it's 100% like me, it's still a robot. Of course it doesn't drink—"

—and that was is where everything went wrong. The robot suddenly hit Lenalee with an anesthetics. Komurin which had the purpose to "make exorcists stronger", believed that it should perform a surgery on Lenalee to make her macho—which gave everyone a scary image in mind.

Later, Allen arrived at the headquarters and found Lenalee's unconscious body, and an injured Reever, a staff from the Science section. While they were running around trying to escape from Komurin's attack, Reever told Allen about the chaos started by Komui's invention "to help exorcists". Just this time Allen figured out that Lenalee was an exorcist as well—which should have been obvious as the white cross symbolized it on her uniform. You can see that they hadn't got to know each other closer yet.

When they met up with Komui and the other staffs, Komui was so desperately trying to save Lenalee as well as Komurin (because they were trying to destroy him) that he tried to use Allen as a bait to buy some time. Komurin took Allen in to perform surgery. Fortunately, Lenalee opened her eyes at the perfect time, just before Komurin got her to perform the macho surgery. :D

The first thing that came to Lenalee's mind was: "I heard Allen-kun's voice... is he back?" Lenalee hadn't known Allen for quite long, but she already memorized his voice. This is a sign that she no longer thought of Allen as a stranger; let alone being inhuman.

Lenalee then activated her Innocence, Dark Boots. It allowed her to move swiftly like a butterfly, and gave a destructive power to her legs. Reever told Lenalee where Allen was, and she began destroying Komurin without a doubt, and Allen was rescued. Komui was shocked to see his invention being crushed by his own sister. When Lenalee was about to give Komurin a finishing blow, Komui caught up to her and tried to protect Komurin, convincing her that Komurin is innocent. Lenalee then kicked Komui because of his selfishness while his invention had caused damages everywhere.

When you think of it again, Komui should be Lenalee's most precious person in the world. However, this time she actually ignored his request and even kicked him along with his creation. This is more than enough proof that Lenalee already accepted Allen in her world.

When Allen came to (after the shock from Komurin's surgery and anesthetics), he found out that Lenalee had been nursing him. She apologized for the troubles her brother's invention had caused, and then gave Allen the Innocence he obtained from the mission before. I'm quite sure she could have taken it to Hevlaska alone, but she felt that Allen might want to experience the accomplishment of his first mission to the very last step, so he gave it back to Allen. Lenalee then smiled softly.

Lenalee: "Welcome home, Allen-kun."
Allen: (blushes) "I-I'm back." (thinks) She's cute.

For Allen, who's lost the only person he considered a "family", Lenalee and the Order's welcome greeting as something really precious. He's lost his "home", and now that somebody new welcomes him, he feels like he's found a new home. He feels accepted. At the same time, he's found his new family.

Also, that was probably the first time Allen took a note towards Lenalee's appearance. :D Actually, this scene resembles one moment in ZONE, the author's debut work in 2003, while the characters were at their prototype stage. It is likely that these two's attraction to one another has been decided ever since that time... who knows.